Recent years have witnessed an explosion of blockchains, each with an open ledger that anyone can read from and write to. In this multi-chain world, an important question emerges: how can we build a more secure overlay blockchain by reading from and writing to a given set of blockchains? Drawing an analogy with switching circuits, we approach the problem by defining two basic compositional operations between blockchains, serial and triangular compositions, and use these operations as building blocks to construct general overlay blockchains. Under the partially synchronous setting, we have the following results: 1) the serial composition, between two certificate-producing blockchains, yields an overlay blockchain that is safe if at least one of the two underlay blockchains is safe and that is live if both of them are live; 2) the triangular composition between three blockchains, akin to parallel composition of switching circuits, yields an overlay blockchain that is safe if all underlay blockchains are safe and that is live if over half of them are live; 3) repeated composition of these two basic operations can yield all possible tradeoffs of safety and liveness for an overlay blockchain built on an arbitrary number of underlay chains. The results are also extended to the synchronous setting.

For Nakamoto's longest-chain consensus protocol, whose proof-of-work (PoW) and proof-of-stake (PoS) variants power major blockchains such as Bitcoin and Cardano, we revisit the classic problem of the security--performance tradeoff: Given a network of nodes with finite communication- and computation-resources, against what fraction of adversary power is Nakamoto consensus (NC) secure for a given block production rate? State-of-the-art analyses of NC fail to answer this question, because their bounded-delay model does not capture the rate limits to nodes' processing of blocks, which cause congestion when blocks are released in quick succession. We develop a new analysis technique to prove a refined security--performance tradeoff for PoW NC in a bounded-capacity model. In this model, we show that, in contrast to the classic bounded-delay model, Nakamoto's private attack is no longer the worst attack, and a new attack we call the teasing strategy, that exploits congestion, is strictly worse. In PoS, equivocating blocks can exacerbate congestion, making traditional PoS NC insecure except at very low block production rates. To counter such equivocation spamming, we present a variant of PoS NC we call Blanking NC (BlaNC), which achieves the same resilience as PoW NC.

The softmax function is ubiquitous in machine learning and optimization applications. Computing the full softmax evaluation of a matrix-vector product can be computationally expensive in high-dimensional settings. In many applications, however, it is sufficient to calculate only the top few outputs of the softmax function. In this work, we present an algorithm, dubbed AdaptiveSoftmax, that adaptively computes the top k softmax values more efficiently than the full softmax computation, with probabilistic guarantees. We demonstrate the sample efficiency improvements afforded by AdaptiveSoftmax on real and synthetic data to corroborate our theoretical results. AdaptiveSoftmax yields >10x gain over full softmax computation on most datasets, yielding up to 30x improvement for Mistral7B evaluated on the Wikitext dataset. The adaptive method we propose for estimating the partition function (the softmax denominator) is of independent interest and can be used in other applications such as kernel density estimation.

Classic BFT consensus protocols guarantee safety and liveness for all clients if fewer than one-third of replicas are faulty. However, in applications such as high-value payments, some clients may want to prioritize safety over liveness. Flexible consensus allows each client to opt for higher safety resilience, albeit at the expense of reduced liveness resilience. We present the first construction that allows optimal safety–liveness tradeoff for every client simultaneously. This construction is modular and is realized as an add-on applied on top of an existing consensus protocol. The add-on consists of an additional round of voting and permanent locking done by the replicas, to sidestep a sub-optimal quorum-intersection-based constraint present in previous solutions. We adapt our construction to the existing Ethereum protocol to derive optimal flexible confirmation rules that clients can adopt unilaterally without requiring system-wide changes. This is possible because existing Ethereum protocol features can double as the extra voting and locking. We show an implementation using Ethereum’s consensus API.

Fourteen years after the invention of Bitcoin, there has been a proliferation of many permissionless blockchains. Each such chain provides a public ledger that can be written to and read from by anyone. In this multi-chain world, a natural question arises: what is the optimal security an existing blockchain, a consumer chain, can extract by only reading and writing to k other existing blockchains, the provider chains? We design a protocol, called interchain timestamping, and show that it extracts the maximum economic security from the provider chains, as quantified by the slashable safety resilience. We observe that interchain timestamps are already provided by light-client based bridges, so interchain timestamping can be readily implemented for Cosmos chains connected by the Inter-Blockchain Communication (IBC) protocol. We compare interchain timestamping with cross-staking, the original solution to mesh security, as well as with Trustboost, another recent security sharing protocol.

Bitcoin is the most secure blockchain in the world, supported by the immense hash power of its Proof-of-Work miners. Proof-of-Stake chains are energy-efficient, have fast finality but face several security issues: susceptibility to non-slashable long-range safety attacks, low liveness resilience and difficulty to bootstrap from low token valuation. We show that these security issues are inherent in any PoS chain without an external trusted source, and propose a new protocol, Babylon, where an off-the-shelf PoS protocol checkpoints onto Bitcoin to resolve these issues. An impossibility result justifies the optimality of Babylon. A use case of Babylon is to reduce the stake withdrawal delay: our experimental results show that this delay can be reduced from weeks in existing PoS chains to less than 5 hours using Babylon, at a transaction cost of less than 10K USD per annum for posting the checkpoints onto Bitcoin.

The ability to verifiably retrieve transaction or state data stored off-chain is crucial to blockchain scaling techniques such as rollups or sharding. We formalize the problem and design a storage- and communication-efficient protocol using linear erasure-correcting codes and homomorphic vector commitments. Motivated by application requirements for rollups, our solution Semi-AVID-PR departs from earlier Verifiable Information Dispersal schemes in that we do not require comprehensive termination properties. Compared to Data Availability Oracles, under no circumstance do we fall back to returning empty blocks. Distributing a file of 22 MB among 256 storage nodes, up to 85 of which may be adversarial, requires in total ≈ 70MB of communication and storage, and ≈ 41 s of single-thread runtime (< 3 s on 16 threads) on an AMD Opteron 6378 processor when using the BLS12-381 curve. Our solution requires no modification to on-chain contracts of Validium rollups such as StarkWare's StarkEx. Additionally, it provides privacy of the dispersed data against honest-but-curious storage nodes. We discuss an application of our Semi-AVID-PR scheme to data availability verification schemes based on random sampling.

Spamming attacks are a serious concern for consensus protocols, as witnessed by recent outages of a major blockchain, Solana. They cause congestion and excessive message delays in a real network due to its bandwidth constraints. In contrast, longest chain (LC), an important family of consensus protocols, has previously only been proven secure assuming an idealized network model in which all messages are delivered within bounded delay. This model-reality mismatch is further aggravated for Proof-of-Stake (PoS) LC where the adversary can spam the network with equivocating blocks. Hence, we extend the network model to capture bandwidth constraints, under which nodes now need to choose carefully which blocks to spend their limited download budget on. To illustrate this point, we show that 'download along the longest header chain', a natural download rule for Proof-of-Work (PoW) LC, is insecure for PoS LC. We propose a simple rule 'download towards the freshest block', formalize two common heuristics 'not downloading equivocations' and 'blocklisting', and prove in a unified framework that PoS LC with any one of these download rules is secure in bandwidth-constrained networks. In experiments, we validate our claims and showcase the behavior of these download rules under attack. By composing multiple instances of a PoS LC protocol with a suitable download rule in parallel, we obtain a PoS consensus protocol that achieves a constant fraction of the network's throughput limit even under worst-case adversarial strategies.

We study the problem of estimating the value of a known smooth function f at an unknown point $\mu \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of $\mu$ corresponding to directions of the function with larger directional derivatives is more sample-efficient. However, as $\mu$ is unknown, the optimal sampling frequencies are also unknown. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-\delta$ returns an $\epsilon$ accurate estimate of $f(\mu)$. We generalize our algorithm to adapt to heteroskedastic noise, and prove asymptotic optimality when f is linear. We corroborate our theoretical results with numerical experiments, showing the dramatic gains afforded by adaptivity.

In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution, and each arm can be sampled further to obtain noisy estimates of the average reward of that arm. Prior work focuses on the best arm, i.e. estimating the maximum of the average reward distribution. We consider a general class of distribution functionals beyond the maximum and obtain optimal sample complexities in both offline and online settings. We show that online estimation, where the learner can sequentially choose whether to sample a new or existing arm, offers no advantage over the offline setting for estimating the mean functional, but significantly reduces the sample complexity for other functionals such as the median, maximum, and trimmed mean. We propose unified meta algorithms for the online and offline settings and derive matching lower bounds using different Wasserstein distances. For the special case of median estimation, we identify a curious thresholding phenomenon on the indistinguishability between Gaussian convolutions with respect to the noise level, which may be of independent interest.

The CAP theorem says that no blockchain can be live under dynamic participation and safe under temporary network partitions. To resolve this availability-finality dilemma, we formulate a new class of flexible consensus protocols, ebb-and-flow protocols, which support a full dynamically available ledger in conjunction with a finalized prefix ledger. The finalized ledger falls behind the full ledger when the network partitions but catches up when the network heals. Gasper, the current candidate protocol for Ethereum 2.0’s beacon chain, combines the finality gadget Casper FFG with the LMD GHOST fork choice rule and aims to achieve this property. However, we discovered an attack in the standard synchronous network model, highlighting a general difficulty with existing finality-gadget-based designs. We present a construction of provably secure ebb-and-flow protocols with optimal resilience. Nodes run an off-the-shelf dynamically available protocol, take snapshots of the growing available ledger, and input them into a separate off-the-shelf BFT protocol to finalize a prefix. We explore connections with flexible BFT and improve upon the state-of-the-art for that problem.

Nakamoto invented the longest chain protocol, and claimed its security by analyzing the private double-spend attack, a race between the adversary and the honest nodes to grow a longer chain. But is it the worst attack? We answer the question in the affirmative for three classes of longest chain protocols, designed for different consensus models: 1) Nakamoto's original Proof-of-Work protocol; 2) Ouroboros and SnowWhite Proof-of-Stake protocols; 3) Chia Proof-of-Space protocol. As a consequence, exact characterization of the maximum tolerable adversary power is obtained for each protocol as a function of the average block time normalized by the network delay. The security analysis of these protocols is performed in a unified manner by a novel method of reducing all attacks to a race between the adversary and the honest nodes.

Generative Adversarial Networks (GANs) are a thriving unsupervised machine learning technique that has led to significant advances in various fields such as computer vision, natural language processing, among others. However, GANs are known to be difficult to train and usually suffer from mode collapse and the discriminator winning problem. To interpret the empirical observations of GANs and design better ones, we deconstruct the study of GANs into three components and make the following contributions. Formulation: we propose a perturbation view of the population target of GANs. Building on this interpretation, we show that GANs can be connected to the robust statistics framework, and propose a novel GAN architecture, termed as Cascade GANs, to provably recover meaningful low-dimensional generator approximations when the real distribution is high-dimensional and corrupted by outliers. Generalization: given a population target of GANs, we design a systematic principle, projection under admissible distance, to design GANs to meet the population requirement using only finite samples. We implement our principle in three cases to achieve polynomial and sometimes near-optimal sample complexities: (1) learning an arbitrary generator under an arbitrary pseudonorm; (2) learning a Gaussian location family under total variation distance, where we utilize our principle to provide a new proof for the near-optimality of the Tukey median viewed as GANs; (3) learning a low-dimensional Gaussian approximation of a high-dimensional arbitrary distribution under Wasserstein distance. We demonstrate a fundamental trade-off in the approximation error and statistical error in GANs, and demonstrate how to apply our principle in practice with only empirical samples to predict how many samples would be sufficient for GANs in order not to suffer from the discriminator winning problem. Optimization: we demonstrate alternating gradient descent is provably not locally asymptotically stable in optimizing the GAN formulation of PCA. We found that the minimax duality gap being non-zero might be one of the causes, and propose a new GAN architecture whose duality gap is zero, where the value of the game is equal to the previous minimax value (not the maximin value). We prove the new GAN architecture is globally asymptotically stable in solving PCA under alternating gradient descent.

The concept of a blockchain was invented by Satoshi Nakamoto to maintain a distributed ledger. In addition to its security, important performance measures of a blockchain protocol are its transaction throughput and confirmation latency. In a decentralized setting, these measures are limited by two underlying physical network attributes: communication capacity and speed-of-light propagation delay. In this work we introduce Prism, a new proof-of-work blockchain protocol, which can achieve 1) security against up to 50% adversarial hashing power; 2) optimal throughput up to the capacity C of the network; 3) confirmation latency for honest transactions proportional to the propagation delay D, with confirmation error probability exponentially small in the bandwidth-delay product CD; 4) eventual total ordering of all transactions. Our approach to the design of this protocol is based on deconstructing Nakamoto's blockchain into its basic functionalities and systematically scaling up these functionalities to approach their physical limits.

Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large number of hypothesis tests need to be performed simultaneously, it is rarely used due to its prohibitive computational cost. In genome-wide association studies, for example, the number of hypothesis tests $m$ is around $10^6$ while the number of MC samples $n$ for each test could be greater than $10^8$, totaling more than $nm$=$10^{14}$ samples. In this paper, we propose \texttt{A}daptive \texttt{M}C multiple \texttt{T}esting (\texttt{AMT}) to estimate MC p-values and control false discovery rate in multiple testing. The algorithm outputs the same result as the standard full MC approach with high probability while requiring only $\tilde{O}(\sqrt{n}m)$ samples. This sample complexity is shown to be optimal. On a Parkinson GWAS dataset, the algorithm reduces the running time from 2 months for full MC to an hour. The \texttt{AMT} algorithm is derived based on the theory of multi-armed bandits.

In this paper, we propose a polar coding scheme for parallel Gaussian channels. The encoder knows the sum capacity of the parallel channels (the capacity of each channel is assumed to be fractional) but does not know the capacity of any channel. By using the nesting property of polar codes, we design a coding/decoding scheme to achieve the sum capacity.

The medoid of a set of n points is the point in the set that minimizes the sum of distances to other points. It can be determined exactly in O(n^2) time by computing the distances between all pairs of points. Previous works show that one can significantly reduce the number of distance computations needed by adaptively querying distances. The resulting randomized algorithm is obtained by a direct conversion of the computation problem to a multi-armed bandit statistical inference problem. In this work, we show that we can better exploit the structure of the underlying computation problem by modifying the traditional bandit sampling strategy and using it in conjunction with a suitably chosen multi-armed bandit algorithm. Four to five orders of magnitude gains over exact computation are obtained on real data, in terms of both number of distance computations needed and wall clock time. Theoretical results are obtained to quantify such gains in terms of data parameters. Our code is publicly available online at https://github.com/TavorB/Correlated-Sequential-Halving.

Computing the medoid of a large number of points in high-dimensional space is an increasingly common operation in many data science problems. We present an algorithm Med-dit to compute the medoid with high probability, which uses $O(n\log n)$ distance evaluations. Med-dit is based on a connection with the Multi-Armed Bandit problem. We evaluate the performance of Med-dit empirically on the Netflix-prize and single-cell RNA-seq datasets, containing hundreds of thousands of points living in tens of thousands of dimensions, and observe a $5$-$10$x improvement in performance over the current state of the art. We have released the code of Med-dit and our empirical results at https://github.com/bagavi/Meddit.

Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative model minimizing a divergence measure, e.g. the Jensen-Shannon (JS) divergence, to the data distribution. However, in practice the discriminator is constrained to be in a smaller class F such as neural nets. Then, a natural question is how the divergence minimization interpretation changes as we constrain F. In this work, we address this question by developing a convex duality framework for analyzing GANs. For a convex set F, this duality framework interprets the original GAN formulation as finding the generative model with minimum JS-divergence to the distributions penalized to match the moments of the data distribution, with the moments specified by the discriminators in F. We show that this interpretation more generally holds for f-GAN and Wasserstein GAN. As a byproduct, we apply the duality framework to a hybrid of f-divergence and Wasserstein distance. Unlike the f-divergence, we prove that the proposed hybrid divergence changes continuously with the generative model, which suggests regularizing the discriminator's Lipschitz constant in f-GAN and vanilla GAN. We numerically evaluate the power of the suggested regularization schemes for improving GAN's training performance.

Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes analyzing their performance challenging. In this paper, we take another approach to this problem by constraining the network such that the corresponding optimization landscape has good theoretical properties without significantly compromising performance. In particular, for two-layer neural networks we introduce Porcupine Neural Networks (PNNs) whose weight vectors are constrained to lie over a finite set of lines. We show that most local optima of PNN optimizations are global while we have a characterization of regions where bad local optimizers may exist. Moreover, our theoretical and empirical results suggest that an unconstrained neural network can be approximated using a polynomially-large PNN.

BACKGROUND: With the recent proliferation of single-cell RNA-Seq experiments, several methods have been developed for unsupervised analysis of the resulting datasets. These methods often rely on unintuitive hyperparameters and do not explicitly address the subjectivity associated with clustering. RESULTS: In this work, we present DendroSplit, an interpretable framework for analyzing single-cell RNA-Seq datasets that addresses both the clustering interpretability and clustering subjectivity issues. DendroSplit offers a novel perspective on the single-cell RNA-Seq clustering problem motivated by the definition of "cell type", allowing us to cluster using feature selection to uncover multiple levels of biologically meaningful populations in the data. We analyze several landmark single-cell datasets, demonstrating both the method's efficacy and computational efficiency. CONCLUSION: DendroSplit offers a clustering framework that is comparable to existing methods in terms of accuracy and speed but is novel in its emphasis on interpretabilty. We provide the full DendroSplit software package at https://github.com/jessemzhang/dendrosplit .

We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating an independent message to its own destination, subject to the capacity constraints on the directed edges of the network. We propose a simple outer bound for the problem that we call the generalized network sharing (GNS) bound. We show that this bound is the tightest edge-cut bound for two-unicast networks and is tight in several cases, though it is not tight in general. We also show that the problem of computing the GNS bound is NP complete. Finally, we show that despite its seeming simplicity, the two-unicast problem is a very difficult problem: the general network coding problem can be reduced to two-unicast. As a consequence, linear coding is insufficient to achieve capacity for general two-unicast networks, and non-Shannon inequalities are necessary for characterizing the capacity of general two-unicast networks.

Due to its longevity and enormous information density, DNA is an attractive medium for archival storage. In this work, we study the fundamental limits and tradeoffs of DNA-based storage systems under a simple model, motivated by current technological constraints on DNA synthesis and sequencing. Our model captures two key distinctive aspects of DNA storage systems: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the data is read by randomly sampling from this DNA pool. Under this model, we characterize the storage capacity, and show that a simple index-based coding scheme is optimal.

Two-way communication is prevalent and its fundamental limits are first studied in the point-to-point setting by Shannon. One natural extension is a two-way interference channel (IC) with four independent messages: two associated with each direction of communication. In this paper, we explore a deterministic two-way IC, which captures the key properties of the wireless Gaussian channel. Our main contribution lies in the complete capacity region characterization of the two-way IC (with respect to the forward and backward sum-rate pair) via a new achievable scheme and a new converse. One surprising consequence of this result is that not only we can get an interaction gain over the one-way non-feedback capacities, we can sometimes get all the way to perfect feedback capacities in both directions simultaneously. In addition, our novel outer bound characterizes channel regimes in which interaction has no bearing on capacity.

Consider a dataset where data is collected on multiple features of multiple individuals over multiple times. This type of data can be represented as a three dimensional individual/feature/time tensor and has become increasingly prominent in various areas of science. The tensor biclustering problem computes a subset of individuals and a subset of features whose signal trajectories over time lie in a low-dimensional subspace, modeling similarity among the signal trajectories while allowing different scalings across different individuals or different features. We study the information-theoretic limit of this problem under a generative model. Moreover, we propose an efficient spectral algorithm to solve the tensor biclustering problem and analyze its achievability bound in an asymptotic regime. Finally, we show the efficiency of our proposed method in several synthetic and real datasets.

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait. We have a rich set of features for each variant (e.g. its location, conservation, epigenetics etc.) which could inform how likely the variant is to have a true association. However popular testing approaches, such as Benjamini-Hochberg's procedure (BH) and independent hypothesis weighting (IHW), either ignore these features or assume that the features are categorical. We propose a new algorithm, NeuralFDR, which automatically learns a discovery threshold as a function of all the hypothesis features. We parametrize the discovery threshold as a neural network, which enables flexible handling of multi-dimensional discrete and continuous features as well as efficient end-to-end optimization. We prove that NeuralFDR has strong false discovery rate (FDR) guarantees, and show that it makes substantially more discoveries in synthetic and real datasets. Moreover, we demonstrate that the learned discovery threshold is directly interpretable.

Variant calling, in particular, calling SNPs (Single Nucleotide Polymorphisms) is a fundamental task in genomics. While existing packages offer excellent performance on calling SNPs which have uniquely mapped reads, they suffer in loci where the reads are multiply mapped, and are unable to make any reliable calls. Variants in multiply mapped loci can arise, for example in long segmental duplications, and can play important role in evolution and disease. In this paper, we develop a new SNP caller named abSNP, which offers three innovations. (a) abSNP calls SNPs from RNA-Seq data. Since RNA-Seq data is primarily sampled from gene regions, this method is inexpensive. (b) abSNP is able to successfully make calls on repetitive gene regions by exploiting the quality scores of multiply mapped reads carefully in order to make variant calls. (c) abSNP exploits a specific feature of RNA-Seq data, namely the varying abundance of different genes, in order to identify which repetitive copy a particular read is sampled from. We demonstrate that the proposed method offers significant performance gains on repetitive regions in simulated data. In particular, the algorithm is able to achieve near-perfect sensitivity on high-coverage SNPs, even when multiply mapped.

Motivation: Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure. Our spatial inference algorithm can also be effectively applied to the problem of population stratification in genome-wide association studies (GWAS), where hidden population structure can create fictitious associations when population ancestry is correlated with both the genotype and the trait. Results: Our algorithm Geographic Ancestry Positioning (GAP) relates local genetic distances between samples to their spatial distances, and can be used for visually discerning population structure as well as accurately inferring the spatial origin of individuals on a two-dimensional continuum. On both simulated and several real datasets from diverse human populations, GAP exhibits substantially lower error in reconstructing spatial ancestry coordinates compared to PCA. We also develop an association test that uses the ancestry coordinates inferred by GAP to accurately account for ancestry-induced correlations in GWAS. Based on simulations and analysis of a dataset of 10 metabolic traits measured in a Northern Finland cohort, which is known to exhibit significant population structure, we find that our method has superior power to current approaches. Availability and Implementation: Our software is available at https://github.com/anand-bhaskar/gap . Contacts: [email protected] or [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Motivated by applications in domains such as social networks and computational biology, we study the problem of community recovery in graphs with locality. In this problem, pairwise noisy measurements of whether two nodes are in the same community or different communities come mainly or exclusively from nearby nodes rather than uniformly sampled between all node pairs, as in most existing models. We present two algorithms that run nearly linearly in the number of measurements and which achieve the information limits for exact recovery.

A rateless coding scheme transmits incrementally more and more coded bits over an unknown channel until all the information bits are decoded reliably by the receiver. We propose a new rateless coding scheme based on polar codes, and we show that this scheme is capacity-achieving, i.e. its information rate is as good as the best code specifically designed for the unknown channel. Previous rateless coding schemes are designed for specific classes of channels such as AWGN channels, binary erasure channels, etc. but the proposed rateless coding scheme is capacity-achieving for broad classes of channels as long as they are ordered via degradation. Moreover, it inherits the conceptual and computational simplicity of polar codes.

Earlier formulations of the DNA assembly problem were all in the context of perfect assembly; i.e., given a set of reads from a long genome sequence, is it possible to perfectly reconstruct the original sequence? In practice, however, it is very often the case that the read data is not sufficiently rich to permit unambiguous reconstruction of the original sequence. While a natural generalization of the perfect assembly formulation to these cases would be to consider a rate-distortion framework, partial assemblies are usually represented in terms of an assembly graph, making the definition of a distortion measure challenging. In this work, we introduce a distortion function for assembly graphs that can be understood as the logarithm of the number of Eulerian cycles in the assembly graph, each of which correspond to a candidate assembly that could have generated the observed reads. We also introduce an algorithm for the construction of an assembly graph and analyze its performance on real genomes.

We explore two-way interference channels (ICs) where there are forward and backward ICs with four independent messages: two associated with the forward IC and the other two with respect to the backward IC. For a linear deterministic model of this channel, we develop inner and outer bounds on the capacity region. As a consequence, we demonstrate that interaction across forward and backward channels enables a more beneficial use of the channels, thereby yielding strict capacity improvements over non-interactive independent transmission. Moreover, our novel outer bound establishes the characterization of channel regimes in which interaction has no bearing on sum capacity.

Given a task of predicting Y from X, a loss function L, and a set of probability distributions Gamma on (X,Y), what is the optimal decision rule minimizing the worst-case expected loss over Gamma? In this paper, we address this question by introducing a generalization of the maximum entropy principle. Applying this principle to sets of distributions with marginal on X constrained to be the empirical marginal, we provide a minimax interpretation of the maximum likelihood problem over generalized linear models as well as some popular regularization schemes. For quadratic and logarithmic loss functions we revisit well-known linear and logistic regression models. Moreover, for the 0-1 loss we derive a classifier which we call the minimax SVM. The minimax SVM minimizes the worst-case expected 0-1 loss over the proposed Gamma by solving a tractable optimization problem. We perform several numerical experiments to show the power of the minimax SVM in outperforming the SVM.

MOTIVATION: In the context of third-generation long-read sequencing technologies, read-overlap-based approaches are expected to play a central role in the assembly step. A fundamental challenge in assembling from a read-overlap graph is that the true sequence corresponds to a Hamiltonian path on the graph, and, under most formulations, the assembly problem becomes NP-hard, restricting practical approaches to heuristics. In this work, we avoid this seemingly fundamental barrier by first setting the computational complexity issue aside, and seeking an algorithm that targets information limits In particular, we consider a basic feasibility question: when does the set of reads contain enough information to allow unambiguous reconstruction of the true sequence? RESULTS: Based on insights from this information feasibility question, we present an algorithm-the Not-So-Greedy algorithm-to construct a sparse read-overlap graph. Unlike most other assembly algorithms, Not-So-Greedy comes with a performance guarantee: whenever information feasibility conditions are satisfied, the algorithm reduces the assembly problem to an Eulerian path problem on the resulting graph, and can thus be solved in linear time. In practice, this theoretical guarantee translates into assemblies of higher quality. Evaluations on both simulated reads from real genomes and a PacBio Escherichia coli K12 dataset demonstrate that Not-So-Greedy compares favorably with standard string graph approaches in terms of accuracy of the resulting read-overlap graph and contig N50. AVAILABILITY: Available at github.com/samhykim/nsg CONTACT: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Given low order moment information over the random variables X = (X1, X2, …, Xp) and Y, what distribution minimizes the Hirschfeld-Gebelein-Rényi (HGR) maximal correlation coefficient between X and Y, while remains faithful to the given moments? The answer to this question is important especially in order to fit models over (X, Y) with minimum dependence among the random variables X and Y. In this paper, we investigate this question first in the continuous setting by showing that the jointly Gaussian distribution achieves the minimum HGR correlation coefficient among distributions with the given first and second order moments. Then, we pose a similar question in the discrete scenario by fixing the pairwise marginals of the random variables X and Y. Subsequently, we derive a lower bound for the HGR correlation coefficient over the class of distributions with fixed pairwise marginals. Then we show that this lower bound is tight if there exists a distribution with certain additive structure satisfying the given pairwise marginals. Moreover, the distribution with the additive structure achieves the minimum HGR correlation coefficient. Finally, we conclude by showing that the event of obtaining pairwise marginals containing an additive structured distribution has a positive Lebesgue measure over the probability simplex.

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs).A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.

Superdirectivity has been a controversial idea to increase the resolving power of an antenna aperture and hence increase the number of spatial degrees of freedom. In this paper, we take into account both radiated power and reactive power, and show that superdirectivity does not have a drastic impact on the total number of spatial-temporal degrees of freedom in wireless channels.

While most current high-throughput DNA sequencing technologies generate short reads with low error rates, emerging sequencing technologies generate long reads with high error rates. A basic question of interest is the tradeoff between read length and error rate in terms of the information needed for the perfect assembly of the genome. Using an adversarial erasure error model, we make progress on this problem by establishing a critical read length, as a function of the genome and the error rate, above which perfect assembly is guaranteed. For several real genomes, including those from the GAGE dataset, we verify that this critical read length is not significantly greater than the read length required for perfect assembly from reads without errors.

Consider the binary classification problem of predicting a target variable Y from a discrete feature vector X = (X1,...,Xd). When the probability distribution P(X,Y) is known, the optimal classifier, leading to the minimum misclassification rate, is given by the Maximum A-posteriori Probability (MAP) decision rule. However, in practice, estimating the complete joint distribution P(X,Y) is computationally and statistically impossible for large values of d. Therefore, an alternative approach is to first estimate some low order marginals of the joint probability distribution P(X,Y) and then design the classifier based on the estimated low order marginals. This approach is also helpful when the complete training data instances are not available due to privacy concerns. In this work, we consider the problem of designing the optimum classifier based on some estimated low order marginals of (X,Y). We prove that for a given set of marginals, the minimum Hirschfeld-Gebelein-R´enyi (HGR) correlation principle introduced in [1] leads to a randomized classification rule which is shown to have a misclassification rate no larger than twice the misclassification rate of the optimal classifier. Then, we show that under a separability condition, the proposed algorithm is equivalent to a randomized linear regression approach which naturally results in a robust feature selection method selecting a subset of features having the maximum worst case HGR correlation with the target variable. Our theoretical upper-bound is similar to the recent Discrete Chebyshev Classifier (DCC) approach [2], while the proposed algorithm has significant computational advantages since it only requires solving a least square optimization problem. Finally, we numerically compare our proposed algorithm with the DCC classifier and show that the proposed algorithm results in better misclassification rate over various UCI data repository datasets.

UNLABELLED: We introduce FinisherSC, a repeat-aware and scalable tool for upgrading de novo assembly using long reads. Experiments with real data suggest that FinisherSC can provide longer and higher quality contigs than existing tools while maintaining high concordance. AVAILABILITY AND IMPLEMENTATION: The tool and data are available and will be maintained at http://kakitone.github.io/finishingTool/ CONTACT: : [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Consider the k-unicast network coding problem over an acyclic wireline network: Given a rate vector k-tuple, determine whether the network of interest can support k unicast flows with those rates. It is well known that the one-unicast problem is easy and that it is solved by the celebrated max-flow min-cut theorem. The hardness of k-unicast problems with small k has been an open problem. We show that the two-unicast problem is as hard as any k-unicast problem for k ≥ 3. Our result suggests that the difficulty of a network coding instance is related more to the magnitude of the rates in the rate tuple than to the number of unicast sessions. As a consequence of our result and other well-known results, we show that linear coding is insufficient to achieve capacity, and non-Shannon inequalities are necessary for characterizing capacity, even for two-unicast networks.

We study the information theoretic limits of DNA assembly from paired reads. Each paired read consists of two subsequences of the DNA separated by a certain genomic distance. We show that this problem can be naturally cast as assembly of 2-D jigsaw puzzles. Using this representation, a necessary condition for assembly is derived and is shown to be nearly achieved on several probabilistic genome models.

Recent work identified the fundamental limits on the information requirements in terms of read length and coverage depth required for successful de novo genome reconstruction from shotgun sequencing data, based on the idealistic assumption of no errors in the reads (noiseless reads). In this work, we show that even when there is noise in the reads, one can successfully reconstruct with information requirements close to the noiseless fundamental limit. A new assembly algorithm, X-phased Multibridging, is designed based on a probabilistic model of the genome. It is shown through analysis to perform well on the model, and through simulations to perform well on real genomes.

We study vector space interference alignment for the multiple-input multiple-output interference channel with no time or frequency diversity, and no symbol extensions. We prove both necessary and sufficient conditions for alignment. In particular, we characterize the feasibility of alignment for the symmetric three-user channel where all users transmit along d dimensions, all transmitters have M antennas and all receivers have N antennas, as well as feasibility of alignment for the fully symmetric (M = N) channel with an arbitrary number of users. An implication of our results is that the total degrees of freedom available in a K-user interference channel, using only spatial diversity from the multiple antennas, is at most 2. This is in sharp contrast to the K/2 degrees of freedom shown to be possible by Cadambe and Jafar with arbitrarily large time or frequency diversity. Moving beyond the question of feasibility, we additionally discuss computation of the number of solutions using Schubert calculus in cases where there are a finite number of solutions.

This paper investigates a network coding problem wherein an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than that of an adversary controlling a given number of edges in the network, in that linear codes are insufficient. To solve the node problem, the class of polytope codes is introduced. Polytope codes are constant composition codes operating over bounded polytopes in integer vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that polytope codes achieve a cut-set bound for a class of planar networks. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.

This paper presents system design aspects of a multi-relay half-duplex QMF cooperative system. We propose two simple algorithms that address the design of relay scheduling and inter-relay interference schemes. Proposed linear-complexity scheduling algorithm is proven to be optimal for a multi-relay diamond network under specific channel conditions. We demonstrate through simulations that for typical channel conditions, the achievable QMF rate of a five-relay cooperative system is up to 3 times higher compared to a system without cooperation.

We consider sum-rate edge-cut bounds on network coding rates for the multiple unicast problem. We first show that the Generalized Network Sharing (GNS) bound is equivalent to a functional dependence bound in the literature. After defining a notion of profile of an edge-cut, we show that the only profiles for which, every edge-cut with the said profile leads to a fundamental bound on network coding rates, are the so-called GNS profiles and further, we quantify with a tight constant factor, the amount by which network coding can potentially beat edge-cuts associated with other profiles. Finally, we show that the problem of computing the GNS bound is NP-complete, even for two-unicast networks.

The reference-based DNA shotgun assembly problem is studied from an information-theoretic point of view. The entire sequence has to be assembled based on a reference sequence which is a noisy version of the desired one, and a set of short reads sampled from the desired sequence. Two necessary conditions on the underlying parameters for reconstruction are obtained. A reference-based assembly algorithm is proposed, and it is shown that under these conditions the algorithm can reconstruct the sequence with high probability.

We establish the fundamental limits of DNA shotgun sequencing under noisy reads. We show a surprising result: for the i.i.d. DNA model, noisy reads are as good as noiseless reads, provided that the noise level is below a certain threshold which can be surprisingly high. As an example, for a uniformly distributed DNA sequence and a symmetric substitution noisy read channel, the threshold is as high as 19%.

In this paper we develop a low-complexity coding scheme and system design framework for the half duplex relay channel based on the Quantize-Map-and-Forward (QMF) relaying scheme. The proposed framework allows linear complexity operations at all network terminals. We propose the use of binary LDPC codes for encoding at the source and LDGM codes for mapping at the relay. We express joint decoding at the destination as a belief propagation algorithm over a factor graph. This graph has the LDPC and LDGM codes as subgraphs connected via probabilistic constraints that model the QMF relay operations. We show that this coding framework extends naturally to the high SNR regime using bit interleaved coded modulation (BICM). We develop density evolution analysis tools for this factor graph and demonstrate the design of practical codes for the half-duplex relay channel that perform within 1dB of information theoretic QMF threshold.

We consider a large distributed MIMO system where wireless users with single transmit and receive antenna cooperate in clusters to form distributed transmit and receive antenna arrays. We characterize how the capacity of the distributed MIMO transmission scales with the number of cooperating users, the area of the clusters and the separation between them, in a line-of-sight propagation environment. We use this result to answer the following question: can distributed MIMO provide significant capacity gain over traditional multi-hop in large ad hoc networks with n source-destination pairs randomly distributed over an area A? Two diametrically opposite answers [24] and [26] have emerged in the current literature. We show that neither of these two results are universal and their validity depends on V the relation between the number of users n and √A/λ, which we identify as the spatial degrees of freedom in the network. λ is the carrier wavelength. When √A/λ ≥ n, there are n degrees of freedom in the network and distributed MIMO with hierarchical cooperation can achieve a capacity scaling linearly in n as in [24], while capacity of multihop scales only as √n. On the other hand, when √A/λ ≤ √n as in [26], there are only √n degrees of freedom in the network and they can be readily achieved by multihop. Our results also reveal a third regime where √n ≤ √A/λ ≤ n. Here, the number of degrees of freedom are smaller than n but larger than what can be achieved by multi-hop. We construct scaling optimal architectures for this intermediate regime.

The capacity per unit cost, or, equivalently, the minimum cost to transmit one bit, is a well-studied quantity under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, the minimum cost to transmitBbits of information asynchronously is shown to be equal to (B +H̅)ksync, whereksyncis the synchronous minimum cost per bit and H̅ is a measure of timing uncertainty equal to the entropy for most reasonable arrival time distributions. This result holds when the transmitter can stay idle at no cost and is a particular case of a general result which holds for arbitrary cost functions.

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. A basic question is: given a sequencing technology and the statistics of the DNA sequence, what is the minimum number of reads required for reliable reconstruction? This number provides a fundamental limit to the performance of any assembly algorithm. For a simple statistical model of the DNA sequence and the read process, we show that the answer admits a critical phenomenon in the asymptotic limit of long DNA sequences: if the read length is below a threshold, reconstruction is impossible no matter how many reads are observed, and if the read length is above the threshold, having enough reads to cover the DNA sequence is sufficient to reconstruct. The threshold is computed in terms of the Renyi entropy rate of the DNA sequence. We also study the impact of noise in the read process on the performance.

We study the problem of compressing a source sequence in the presence of side-information that is related to the source via insertions, deletions and substitutions. We propose a simple algorithm to compress the source sequence when the side-information is present at both the encoder and decoder. A key attribute of the algorithm is that it encodes the edits contained in runs of different extents separately. For small insertion and deletion probabilities, the compression rate of the algorithm is shown to be asymptotically optimal.

DNA sequencing is the basic workhorse of modern day biology and medicine. Shotgun sequencing is the dominant technique used: many randomly located short fragments called reads are extracted from the DNA sequence, and these reads are assembled to reconstruct the original sequence. By drawing an analogy between the DNA sequencing problem and the classic communication problem, we define an information theoretic notion of sequencing capacity. This is the maximum number of DNA base pairs that can be resolved reliably per read, and provides a fundamental limit to the performance that can be achieved by any assembly algorithm. We compute the sequencing capacity explicitly for a simple statistical model of the DNA sequence and the read process.

We consider two-way interference channels (ICs) where forward and backward channels are ICs but not necessarily the same. We first consider a scenario where there are only two forward messages and feedback is offered through the backward IC for aiding forward-message transmission. For a linear deterministic model of this channel, we develop inner and outer bounds that match for a wide range of channel parameters. We find that the backward IC can be more efficiently used for feedback rather than if it were used for independent backward-message transmission. As a consequence, we show that feedback can provide a net increase in capacity even if feedback cost is taken into consideration. Moreover we extend this to a more general scenario with two additional independent backward messages, from which we find that interaction can provide an arbitrarily large gain in capacity.

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser multiple-input multiple-output (MIMO) and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in an MIMO broadcast channel with$K$transmit antennas and$K$receivers each with 1 receive antenna,${{K}\over{1+{{1}\over{2}}+\ldots+{{1}\over{K}}}}(>1)$degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.

This paper considers a random access system where each sender is in one of two possible states, active or not active, and the states are only known to the common receiver. Active senders encode data into independent information streams, a subset of which is decoded depending on the collective interference. An information-theoretic formulation of the problem is presented and the set of achievable rates is characterized with a guaranteed gap to optimality. Inner and outer bounds on the capacity region of a two-sender system are tight in the case of a binary-expansion deterministic channel and differ by less than one bit in the case of a Gaussian channel. In systems with an arbitrary number of senders, the symmetric scenario of equal access probabilities and received power constraints is studied and the system throughput, i.e., the maximum achievable expected sum rate, is characterized. It is shown that a simple coding scheme where active senders transmit a single message is optimum for a binary-expansion deterministic channel and achieves within one bit of the optimum in the case of a Gaussian channel. Finally, a comparison with the slotted ALOHA protocol is provided, showing that encoding rate adaptation at the transmitters achieves constant (rather than zero) throughput as the number of users tends to infinity.

Despite considerable progress, the capacity region of fading broadcast channels with channel state known at the receivers but unknown at the transmitter remains unresolved. We address this subject by introducing a layered erasure broadcast channel model in which each component channel has a state that specifies the received signal levels in an instance of a deterministic binary expansion channel. We find the capacity region of this class of broadcast channels. The capacity achieving strategy assigns each signal level to the user that derives the maximum weighted expected rate. The outer bound is based on a channel enhancement that creates a degraded broadcast channel for which the capacity region is known. This same approach is then used to find inner and outer bounds to the capacity region of fading Gaussian broadcast channels. The achievability scheme employs a superposition of binary inputs. For intermittent additive white Gaussian noise (AWGN) channels and for Rayleigh fading channels, the achievable rates are observed to be within 1–2 bits of the outer bound at high SNR. We also prove that the achievable rate region is within 6.386 bits/s/Hz of the capacity region for all fading AWGN broadcast channels.

The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable rate regions when treating interference as noise, using successive interference cancellation decoding, and using joint decoding. In a spatial network where the nodes are distributed according to a Poisson point process and the channel path loss exponent is β >; 2, it is shown that the density of users that can be supported by treating interference as noise can scale no faster than B2/βas the bandwidth B grows, while the density of users can scale linearly with B under optimal decoding.

The problem of reconstructing a source sequence with the presence of decoder side-information that is mis-synchronized to the source due to deletions is studied in a distributed source coding framework. Motivated by practical applications, the deletion process is assumed to be bursty and is modeled by a Markov chain. The minimum rate needed to reconstruct the source sequence with high probability is characterized in terms of an information theoretic expression, which is interpreted as the amount of information of the deleted content and the locations of deletions, subtracting “nature's secret”, that is, the uncertainty of the locations given the source and side-information. For small bursty deletion probability, the asymptotic expansion of the minimum rate is computed.

We investigate the two unicast flow problem over layered linear deterministic networks with arbitrary number of nodes. When the minimum cut value between each source-destination pair is constrained to be 1, it is obvious that the triangular rate region {(R1, R2) : R1, R2≥ 0, R1+ R2≤ 1} can be achieved, and that one cannot achieve beyond the square rate region {(R1, R2) : R1, R2≥ 0, R1≤ 1, R2≤ 1}. Analogous to the work by Wang and Shroff for wired networks [1], we provide the necessary and sufficient conditions for the capacity region to be the triangular region and the necessary and sufficient conditions for it to be the square region. Moreover, we completely characterize the capacity region and conclude that there are exactly three more possible capacity regions of this class of networks, in contrast to the result in wired networks where only two rate regions are possible. Our achievability scheme is based on linear coding over an extension field with at most four nodes performing special linear coding operations, namely interference neutralization and zero forcing, while all other nodes perform random linear coding.

Determining the feasibility conditions for vector space interference alignment in the K-user MIMO interference channel with constant channel coefficients has attracted much recent attention yet remains unsolved. The main result of this paper is restricted to the symmetric square case where all transmitters and receivers have N antennas, and each user desires d transmit dimensions. We prove that alignment is possible if and only if the number of antennas satisfies N ≥ d(K + 1)/2. We also show a necessary condition for feasibility of alignment with arbitrary system parameters. An algebraic geometry approach is central to the results.

We develop an interference alignment (IA) technique for a downlink cellular system. In the uplink, IA schemes need channel-state-information exchange across base-stations of different cells, but our downlink IA technique requires feedback only within a cell. As a result, the proposed scheme can be implemented with a few changes to an existing cellular system where the feedback mechanism (within a cell) is already being considered for supporting multi-user MIMO. Not only is our proposed scheme implementable with little effort, it can in fact provide substantial gain especially when interference from a dominant interferer is significantly stronger than the remaining interference: it is shown that in the two-isolated cell layout, our scheme provides four-fold gain in throughput performance over a standard multi-user MIMO technique. We also show through simulations that our technique provides respectable gain under a more realistic scenario: it gives approximately 28% gain for a 19 hexagonal wrap-around-cell layout. Furthermore, we show that our scheme has the potential to provide substantial gain for macro-pico cellular networks where pico-users can be significantly interfered with by the nearby macro-BS.

In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First, we propose a deterministic channel model which captures the key wireless properties of signal strength, broadcast and superposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut theorem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and-forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destination decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel parameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast networks, half-duplex networks, and ergodic networks.

The paper establishes the capacity region of the Gaussian interference channel with many transmitter-receiver pairs constrained to use point-to-point codes. The capacity region is shown to be strictly larger in general than the achievable rate regions when treating interference as noise, using successive interference cancellation decoding, and using joint decoding. The gains in coverage and achievable rate using the optimal decoder are analyzed in terms of ensemble averages using stochastic geometry. In a spatial network where the nodes are distributed according to a Poisson point process and the channel path loss exponent is β >; 2, it is shown that the density of users that can be supported by treating interference as noise can scale no faster than B2/βas the bandwidthBgrows, while the density of users can scale linearly with B under optimal decoding.

The interference channel is the simplest communication scenario where multiple autonomous users compete for shared resources. We combine game theory and information theory to define the notion of a Nash equilibrium region of the interference channel. The notion is game theoretic: it captures the selfish behavior of each user as they compete. The notion is also information theoretic: it allows each user to use arbitrary communication strategies as it optimizes its own performance. We give an exact characterization of the Nash equilibrium region of the two-user linear deterministic interference channel and an approximate characterization of the Nash equilibrium region of the two-user Gaussian interference channel to within 1 bit/s/Hz.

The fully connectedK-user interference channel is studied in a multipath environment with bandwidthW. We show that when each link consists ofDphysical paths, the total spectral efficiency can grow linearly withK. This result holds not merely in the limit of large transmit powerP, but for any fixedP, and is, therefore, a stronger characterization than degrees of freedom. It is achieved via a form of interference alignment in the time domain. A caveat of this result is thatWmust grow withK, a phenomenon we refer to as bandwidth scaling. Our insight comes from examining channels with single path links (D=1), which we refer to as line-of-sight (LOS) links. For such channels, we build a time-indexed interference graph and associate the communication problem with finding its maximum independent set. This graph has a stationarity property that we exploit to solve the problem efficiently via dynamic programming. Additionally, the interference graph enables us to demonstrate the necessity of bandwidth scaling for any scheme operating over LOS interference channels. Bandwidth scaling is then shown to also be a necessary ingredient for interference alignment in theK-user interference channel.

In this paper, we study a Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows between different source-destination pairs. We focus on two-stage relay-interference networks where there are weak cross links, causing the networks to behave like a chain ofZGaussian channels. Our main result is an approximate characterization of the capacity region for such ZZ and ZS networks. We propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This scheme allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. This scheme in conjunction a new network decomposition technique provides the approximate characterization. Our analysis of these Gaussian networks is based on insights gained from an exact characterization of the corresponding linear deterministic model.

Polarization could be the last resource to be exploited for space-limited devices. Over the past years, theoretical studies and experimental work present different conclusions on the potential increase in the number of degrees of freedom from polarization. This paper attempts to unify the different conclusions and provide a mathematical framework that can be applied to any array geometry and channel scattering condition. It shows that the degree-of-freedom gain from using polarimetric antenna elements ranges from 2 to 6 and the gain depends on the array geometry and the channel scattering condition. Sampling techniques and vector multipole decomposition are applied to derive the results.

We consider a communication network and study the problem of designing a high-throughput and low-delay scheduling policy that only requires a polynomial amount of computation at each time step. The well-known maximum weight scheduling policy, proposed by Tassiulas and Ephremides (1992), has favorable performance in terms of throughput and delay but, for general networks, it can be computationally very expensive. A related randomized policy proposed by Tassiulas (1998) provides maximal throughput with only a small amount of computation per step, but seems to induce exponentially large average delay. These considerations raise some natural questions. Is it possible to design a policy with low complexity, high throughput, and low delay for a general network? Does Tassiulas' randomized policy result in low average delay? In this paper, we answer both of these questions negatively. We consider a wireless network operating under two alternative interference models: (a) a combinatorial model involving independent set constraints and (b) the standard SINR (signal to interference noise ratio) model. We show that unlessNP⊆BPP(orP=NPfor the case of determistic arrivals and deterministic policies), and even if the required throughput is a very small fraction of the network's capacity, there does not exist a low-delay policy whose computation per time step scales polynomially with the number of queues. In particular, the average delay of Tassiulas' randomized algorithm must grow super-polynomially. To establish our results, we employ a clever graph transformation introduced by Lund and Yannakakis (1994).

We characterize the capacity region to within 2 bits/s/Hz and the symmetric capacity to within 1 bit/s/Hz for the two-user Gaussian interference channel (IC) with feedback. We develop achievable schemes and derive a new outer bound to arrive at this conclusion. One consequence of the result is that feedback provides multiplicative gain at high signal-to-noise ratio: the gain becomes arbitrarily large for certain channel parameters. This finding is in contrast to point-to-point and multiple-access channels where feedback provides no gain and only bounded additive gain respectively. The result makes use of a linear deterministic model to provide insights into the Gaussian channel. This deterministic model is a special case of the El Gamal-Costa deterministic model and as a side-generalization, we establish the exact feedback capacity region of this general class of deterministic ICs.

Interference is a major issue limiting the performance in wireless networks. Cooperation among receivers can help mitigate interference by forming distributed MIMO systems. The rate at which receivers cooperate, however, is limited in most scenarios. How much interference can one bit of receiver cooperation mitigate? In this paper, we study the two-user Gaussian interference channel with conferencing decoders to answer this question in a simple setting. We identify two regions regarding the gain from receiver cooperation: linear and saturation regions. In the linear region, receiver cooperation is efficient and provides a degrees-of-freedom gain, which is either one cooperation bit buys one over-the-air bit or two cooperation bits buy one over-the-air bit. In the saturation region, receiver cooperation is inefficient and provides a power gain, which is bounded regardless of the rate at which receivers cooperate. The conclusion is drawn from the characterization of capacity region to within two bits/s/Hz, regardless of channel parameters. The proposed strategy consists of two parts: 1) the transmission scheme, where superposition encoding with a simple power split is employed and 2) the cooperative protocol, where one receiver quantize-bin-and-forwards its received signal and the other after receiving the side information decode-bin-and-forwards its received signal.

Interference limits performance in wireless networks and cooperation among receivers or transmitters can help mitigate interference by forming distributed MIMO systems. Earlier work shows how limited receiver cooperation helps mitigate interference. The scenario with transmitter cooperation, however, is more difficult to tackle. In this paper we study the two-user Gaussian interference channel with conferencing transmitters to make progress towards this direction. We characterize the capacity region to within 6.5 bits/s/Hz, regardless of channel parameters. Based on the bounded-gap-to-optimality result, we show that there is an interesting reciprocity between the scenario with conferencing transmitters and the scenario with conferencing receivers and their capacity regions are within a bounded gap to each other. Hence, in the interference-limited regime, the behavior of the benefit brought by transmitter cooperation is the same as that by receiver cooperation.

We develop an interference alignment (IA) technique for a downlink cellular system. In the uplink, IA schemes need channel-state-information exchange across base-stations of different cells, but our downlink IA technique requires feedback only within a cell. As a result, the proposed scheme can be implemented with minimal changes to an existing cellular system where the feedback mechanism (within a cell) is already being considered for supporting multi-user MIMO. Not only is our proposed scheme implementable with little effort, it can in fact provide substantial gain especially when interference from a dominant interferer is significantly stronger than the remaining interference: it is shown that in the two-isolated cell layout, our scheme provides four-fold gain in throughput performance over a standard multi-user MIMO technique. We show through simulations that our technique provides respectable gain under a more realistic scenario: it gives approximately 20% gain for a 19 hexagonal wrap-around-cell layout.

Multi-hop is the traditional architecture for wireless adhoc networks. In this paper, we investigate the potential gains from more sophisticated cooperation in large wireless adhoc networks. While the capacity of multi-hop is limited to ⊖(√(n)) due to interference, we show that a hierarchical cooperation architecture can achieve linear capacity scaling in the number of users n. We also characterize how the cooperation gain is affected when the network is limited in either power or space.

The capacity per unit cost, or equivalently minimum cost to transmit one bit, is a well-studied quantity. It has been studied under the assumption of full synchrony between the transmitter and the receiver. In many applications, such as sensor networks, transmissions are very bursty, with small amounts of bits arriving infrequently at random times. In such scenarios, the cost of acquiring synchronization is significant and one is interested in the fundamental limits on communication without assuming a priori synchronization. In this paper, we show that the minimum cost to transmit B bits of information asynchronously is (B + H̅)ksync, where ksyncis the synchronous minimum cost per bit and H̅ is a measure of timing uncertainty equalling to the entropy for most reasonable arrival time distributions.

Network coding is studied when an unknown subset of nodes in the network is controlled by an adversary. To solve this problem, a new class of codes called Polytope Codes is introduced. Polytope Codes are linear codes operating over bounded polytopes in real vector fields. The polytope structure creates additional complexity, but it induces properties on marginal distributions of code vectors so that validities of codewords can be checked by internal nodes of the network. It is shown that a cut-set bound for a class planar networks can be achieved using Polytope Codes. It is also shown that this cut-set bound is not always tight, and a tighter bound is given for an example network.

We consider a problem of distributed lossy Gaussian source coding with inputs (y1, y2, y3), where y1and y2are positively correlated, y3= y1- cy2, c ≥ 0, and the decoder requires y3with a target distortion. For this problem, known achievable schemes are unboundedly loose. Inspired by results of binary expansion models, we characterize the rate-distortion region within a bounded gap. Treating each source as a multilayer input, an achievable scheme is developed based on the following observations: (i) some middle layers of y1and y2are not needed at the decoder, (ii) the required layers are combined with some unneeded interference information, (iii) linear operations among input layers can unboundedly reduce the load of reporting interference. Showing that the cut-set outer-bound has an unbounded gap, we also establish a new outer-bound to prove the bounded-gap result.

We consider arbitrary traffic patterns in arbitrarily placed extended wireless networks. We provide sufficient conditions for the approximate optimality of multi-hop communication over such networks. For exponential power decay, we show that these sufficient conditions are always satisfied, resulting in a scaling characterization of the entire capacity region for any node placement.

Interference limits performance in wireless networks, and cooperation among receivers or transmitters can help mitigate interference by forming distributed MIMO systems. Earlier work shows how limited receiver cooperation helps mitigate interference. The scenario with transmitter cooperation, however, is more difficult to tackle. In this paper we study the two-user Gaussian interference channel with conferencing transmitters to make progress towards this direction. We characterize the capacity region to within a constant number of bits regardless of channel parameters. Based on the constant-to-optimality result, we show that there is an interesting reciprocity between the scenario with conferencing transmitters and the scenario with conferencing receivers, and their capacity regions are within a constant gap to each other. Hence in the interference-limited regime, the behavior of the benefit brought by transmitter cooperation is the same as that by receiver cooperation.

Recently, Etkin, Tse, and Wang found the capacity region of the two-user Gaussian interference channel to within 1 bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the many-to-one and one-to-many Gaussian interference channels to within a constant number of bits. The result makes use of a deterministic model to provide insight into the Gaussian channel. The deterministic model makes explicit the dimension of signal level. A central theme emerges: the use of lattice codes for alignment of interfering signals on the signal level.

In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes-bandwidth and power-limited-have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, bandwidth, etc., there are three parameters of importance: the short-distance signal-to-noise ratio (SNR), the long-distance SNR, and the power path loss exponent of the environment. Depending on these parameters, we identify four qualitatively different regimes. One of these regimes is especially interesting since it is fundamentally a consequence of the heterogeneous nature of links in a network and does not occur in the point-to-point case; the network capacity is both power and bandwidth limited. This regime has thus far remained hidden due to the limitations of the existing formulation. Existing schemes, either multihop transmission or hierarchical cooperation, fail to achieve capacity in this regime; we propose a new hybrid scheme that achieves capacity.

We consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate to schedule transmissions, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. A game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified: one in which both networks simultaneously schedule all transmissions, one in which the denser network schedules all transmissions and the sparser only schedules a fraction, and one in which both networks schedule only a fraction of their transmissions. The regime of operation depends on the path loss exponent α, the latter regime being desirable but attainable only for α > 4. This suggests that in certain environments, rival wireless networks may end up naturally cooperating. To substantiate our analytical results, we simulate a system where networks iteratively optimize their access probabilities in a greedy manner. We also discuss a distributed scheduling protocol that employs carrier sensing and demonstrate via simulations that again a near cooperative equilibrium exists for sufficiently large α.

The rate-distortion region for the distributed source coding of the three jointly-Gaussian tree-structured sources with the quadratic distortion measure, is characterized within a constant gap. As a simplified counterpart of the Gaussian problem, we first investigate the rate region of a three binary-expanded sources where each pair of the sources have a certain number of the most-significant bits in common, and the central decoder needs to reconstruct each source with a target resolution. Motivated by the result of binary-expansion model, we prove that the achievable region of the quantize-and-binning scheme and the outer-bound of the cooperative scheme has a bounded gap of 2.4771 bits.

In this paper we study the Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We examine this problem for certain regimes of channel values, when one of the cross-links is dominated by noise, resulting in Z and/or S configurations for the networks. For these Gaussian ZZ and ZS networks, we establish an approximate characterization of the rate region. The outer bounds to the capacity regions are established using genie-aided techniques that extend the methods used for the Gaussian interference channel to the relay-interference network. For the inner bound of the ZZ network, we utilize a new interference management scheme, termed interference neutralization, which was inspired by our earlier study of such deterministic networks. This technique allows for over-the-air interference removal, without the transmitters having complete access to the interfering signals.

Cooperation between terminals has been proposed to improve the reliability and throughput of wireless communication. While recent work has shown that relay cooperation provides increased diversity, increased multiplexing gain over that offered by direct link has largely been unexplored. In this work we show that cooperative multiplexing gain can be achieved by using a half duplex relay. We capture relative distances between terminals in the high SNR diversity multiplexing tradeoff (DMT) framework. The DMT performance is then characterized for a network having a single antenna half-duplex relay between a single-antenna source and two-antenna destination. Our results show that the achievable multiplexing gain using cooperation can be greater than that of the direct link and is a function of the relative distance between source and relay compared to the destination. Moreover, for multiplexing gains less than 1, a simple scheme of the relay listening 1/3 of the time and transmitting 2/3 of the time can achieve the 2 by 2 MIMO DMT.

Recent results have shown that interference alignment can achieve K/2 degrees of freedom in a K-user interference channel with time or frequency varying channel coefficients. For fixed number of users K, the number of degrees of freedom characterizes the asymptotic behavior of the performance in the high SNR limit but it does not answer the question of how the performance scales with K for any fixed SNR. In particular, it is unclear if a constant rate per user can be maintained as more users enter into the system. In this paper, we investigate the performance of the interference alignment scheme proposed in for fixed SNR. We assume that the channel coefficients between the users are of the form r ejthetaswhere r is fixed over the duration of communication and thetas is a fast fading phase. We show that for any value of the SNR and K, the aggregate rate achieved by the interference alignment scheme of is lower bounded by c1K log(1 + c2SNR) where c1and c2are positive constants independent of both SNR and K. This result establishes the linear scaling of the interference alignment scheme for the considered random phase channel model.

We characterize the symmetric capacity of the two-user Gaussian interference channel withfeedbackto within 1 bit/s/Hz. The result makes use of a deterministic model to provide insights into the Gaussian channel. We derive a new outer bound to show that a proposed scheme can achieve the symmetric capacity to within one bit for all channel parameters. One consequence of the result is that feedback providesunboundedgain, i.e., the gain becomes arbitrarily large for certain channel parameters. It is a surprising result because feedback has been so far known to provide no gain in memoryless point-to-point channels and only power gain (boundedgain) in the multiple access channels. The gain comes from using feedback to fully exploit the side information provided by the broadcast nature of the wireless medium.

We consider a game theoretic model for two users communicating over an interference channel, in which each user can autonomously select its encoding and decoding strategy with the objective of maximizing its own rate. We give an information theoretic formulation for this game, which enables us to define a Nash equilibrium region that is a natural extension of the information theoretic capacity region of this channel. In previous work, we completely characterized this Nash equilibrium region for a deterministic interference channel model. Here, we show that certain properties of this analysis extend to a Gaussian channel model. In particular, we show that for a symmetric channel, the symmetric sum-rate point is always achieved as an approximate equilibrium.

The wireless multiple-unicast problem is considered over a layered network, where the rates of transmission are limited by the relaying and interference effect. The deterministic model introduced is used to capture the broadcasting and multiple access effects. The capacity region of the Z-chain relay-interference network is fully characterized. In order to solve the problem, we introduce a new achievability scheme based on ldquointerference neutralizationrdquo and a new analysis technique to bound the number of non-interfering (pure) signals.

The optimal diversity-multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion-with a small modification to the transmit scheme.

This book provides a thorough coverage of wireless communication fundamentals, with emphasis on information-theoretic concepts. Some of the topics covered include: mathematical models for the physical channel; digital communication and the concept of diversity transmission for fading channels; cellular systems; capacity of wireless channels; multi-user capacity and opportunistic communication; and an extensive treatment of MIMO systems. The list of references is extensive and the index has been prepared with considerable care. The book would make an ideal resource for graduate students seeking a first exposure to the field.

We consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate with one another, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. In this vein a game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified; a full-spread regime, where both networks choose to simultaneously schedule all transmissions; a partial-spread regime, where one network schedules all transmissions and the other only schedules a fraction; and a joint-spread regime, where both networks schedule a fraction of their transmissions. The regime of operation depends on the pathloss exponent alpha. The joint-spread regime, which has a cooperative flavor, is attainable only for alpha > 4, which suggests that in certain environments there may be a natural incentive for rival wireless networks to cooperate.

We present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters.

We provide a natural formulation of information theoretic games on interference channels. We analyze this game on a class of deterministic interference channels recently introduced to approximate Gaussian channels in the interference-limited regime. Our main result is a complete and simple characterization of the subset of the interference channel capacity region that can be achieved as Nash equilibria. We show that for all parameter values of the interference channel, there are always Nash equilibria which are efficient, i.e. on the boundary of the capacity region.

In analyzing the point-to-point wireless channel, insights about two qualitatively different operating regimes-bandwidth- and power-limited-have proven indispensable in the design of good communication schemes. In this paper, we propose a new scaling law formulation for wireless networks that allows us to develop a theory that is analogous to the point-to-point case. We identify fundamental operating regimes of wireless networks and derive architectural guidelines for the design of optimal schemes. Our analysis shows that in a given wireless network with arbitrary size, area, power, etc., there are three parameters of importance: the short-distance SNR, the long-distance SNR, and the power path loss exponent. Depending on these parameters we identify four qualitatively different regimes. One of these regimes is especially interesting since it is fundamentally a consequence of the heterogeneous nature of links in a network and does not occur in the point-to-point case; the network capacity is both power- and bandwidth-limited. This regime has thus far remained hidden due to the limitations of the existing formulation. Existing schemes, either multihop transmission or hierarchical cooperation, fail to achieve capacity in this regime; we propose a new hybrid scheme that achieves capacity.

This paper unifies the different conclusions on the polarization degrees of freedom in multiple-antenna channels. It shows that the multiplicative gain in the degrees of freedom from polarization depends on the array geometry and the scattering condition.

We examine secret communication over interference channels, starting with a model in which communication is semi-secret in that secrecy may depend on other transmitters to follow an agreed-upon signaling strategy. We compare this to robustly-secret communication, in which each user must allow for other users to deviate unilaterally from an agreed-upon strategy to enable better overhearing, as long as that alternate strategy impairs neither the secrecy rate of its own link nor the reliability of any other communicating links. For a particular two-user binary expansion deterministic interference channel, we find and compare the semi-secret and robustly-secret capacity regions.

The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

In data communication networks, packets that arrive at the receiving host may be disordered for reasons such as retransmission of dropped packets or multipath routing. Reliable protocols such as the Transmission Control Protocol (TCP) require packets to be accepted, i.e., delivered to the receiving application, in the order they are transmitted at the sender. In order to do so, the receiver's transport layer is responsible for temporarily buffering out-of-order packets and resequencing them as more packets arrive. In this paper, we analyze a model where the disordering is caused by multipath routing. Packets are generated according to a Poisson process. Then, they arrive at a disordering network (DN) modeled by two parallel M/M/l queues, and are routed to each of the queues according to an independent Bernoulli process. A resequencing buffer follows the DN. In such a model, the packet resequencing delay is known. However, the size of the resequencing queue (RSQ) is unknown. We derive the probability for the large deviations of the queue size.

The discrepancy between perceived spectrum shortage from the FCC allocation map and the actual abundance of available spectrum is a motivation for Cognitive Radios, which locate and transmit in the unused or lightly used bands. If a digital approach is taken to provide the necessary radio flexibility to exploit this sparsity, there is a challenging dynamic range requirement in the analog to digital conversion, since there are large interfering signals which are effectively in-band and can not be removed by fixed RF pre-filtering. Using a mixed analog digital system architecture which uses multiple low accuracy ADCs with digital adaptive filters, it is possible to increase the effective dynamic range of the input by subtracting off the unwanted signals in the time domain.

n source and destination pairs randomly located in a fixed area want to communicate with each other. It is well known that classical multihop architectures that decode and forward packets can deliver at most a radicn-scaling of the aggregate throughput. The performance is limited by the mutual interference between communicating nodes. We show however that a linear scaling of the capacity with n can in fact be achieved by more intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.

The characterization of the capacity region of the two-user Gaussian interference channel has been an open problem for thirty years. The understanding on this problem has been limited. The best known achievable region is due to Han-Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we extend our results of [1] to general (i.e. possibly asymmetric) channels for the complete capacity region. We show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a simplified Han-Kobayashi type scheme can achieve to within a single bit the capacity for all values of the channel parameters. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

In this paper, we study the potential benefit of base-station (BS) cooperation for downlink transmission in a modified Wyner-type multicell model. Besides the dirty-paper-coding (DPC) precoder, we also analyze several linear precoding schemes, including co-phasing, zero-forcing (ZF) and MMSE precoders. For the nonfading case, analytical sum rate expression is obtained for each scheme. In networks of a large number N of cells, a high signal-to-noise-ratio (SNR) asymptotic gap is shown between the sum rate performances of DPC and ZF precoders. Moreover, the MMSE precoder sum rate expression in large networks indicates different behaviors of MMSE precoder in different SNR regimes: in the SNR > N2regime, it coincides with the ZF precoder, while, in the SNR2regime, it coincides with the co-phasing precoder. For the Rayleigh fading case, Monte-Carlo simulations demonstrate the effectiveness of linear precoding schemes with the proposed user selection criterion.

"THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD" In this paper, we employ a broadcast transmission strategy for studying multiple access communication with no channel state information (CSI) at the transmitter. Users simultaneously encode their data into several streams that are then superimposed on top of each other. The receiver decodes a subset of the transmitted streams, dependent on the quality of the channel. We focus on two particular problems: first, we analyze communication over a Gaussian multiple access channel (MAC) with slow fading and no transmitter CSI. Users encode one stream per each fading state. We characterize the fundamental tradeoff between the achievable sum-rates in the various data streams. Next, we study transmission over a two- user synchronous Gaussian MAC in which users transmit in an uncoordinated and random manner. Each user superimposes two data streams, one high priority, ensuring part of the information is received reliably, and one high rate, opportunistically taking advantage of the channel when the other user is not transmitting. We study the performance limit for low and high SNR regimes.

n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r-αand random phase changes. Classical multihop architectures that decode and forward packets can deliver a √n-scaling of the aggregate throughput, while recently proposed hierarchical cooperation achieves n2-α/2-scaling, which is superior to multi-hop for α4, while the moderate-attenuation regime (2 ≤ α ≤ 4) remains uncharacterized. We close this gap by deriving a tight upper bound on the scaling of the aggregate throughput, valid for all α ≥ 2. Our result shows that the mentioned schemes are scaling-optimal, namely that no other scheme can beat hierarchical cooperation when α < 3, nor can it beat classical multi-hop when α ≥ 3. The key ingredient is a careful evaluation of the scaling of the cut-set bound.

In this paper we study channels where a side-information sequence is available strictly causally at the transmitter, i.e., the channel input at time k may depend on the side-information sequence up to and including time k - 1. This is in contrast to Shannon's channel coding with causal side-information at the transmitter where the channel input at time k may depend on the side-information sequence up to and including time k. We consider side-information sequences with memory and study the Gaussian and modulo-additive channels.

We prove a new outer bound to the capacity region of a certain class of interference channels, and quantify the gap between it and the Han-Kobayashi inner bound. The new bound allows the recovery of the El Gamal-Costa characterization of the capacity region of certain deterministic interference channels, and also the recent characterization by Etkin, Tse and Wang of the capacity region of scalar Gaussian interference channels to within '1 bit'. Moreover, the new bound allows a straightforward generalization of the '1 bit' result to vector Gaussian interference channels.

We present a deterministic channel model which captures several key features of multiuser wireless communication. We consider a model for a wireless network with nodes connected by such deterministic channels , and compute the end-to-end capacity when there is a single source and a single destination and an arbitrary number of relay nodes. This capacity has the interpretation of the in ax-flow min-cut solution of a wireline network naturally associated with the deterministic wireless network.

We study a spectrum sharing problem in an unlicensed band where multiple systems coexist and interfere with each other. Due to asymmetries and selfish system behavior, unfair and inefficient situations may arise. We investigate whether efficiency and fairness can be obtained with self-enforcing spectrum sharing rules. These rules have the advantage of not requiring a central authority that verifies compliance to the protocol. Any self-enforcing protocol must correspond to an equilibrium of a game. We first analyze the possible outcomes of a one shot game, and observe that in many cases an inefficient solution results. However, systems often coexist for long periods and a repeated game is more appropriate to model their interaction. In this repeated game the possibility of building reputations and applying punishments allows for a larger set of self-enforcing outcomes. When this set includes the optimal operating point, efficient, fair, and incentive compatible spectrum sharing becomes possible. We present examples that illustrate that in many cases the performance loss due to selfish behavior is small. We also prove that our results are tight and quantify the best achievable performance in a non-cooperative scenario

To establish a secure communications link between any two transceivers, the communicating parties require some shared secret, or key, with which to encrypt the message so that it cannot be understood by an enemy observer. Using the theory of reciprocity for antennas and electromagnetic propagation, a key distribution method is proposed that uses the ultrawideband (UWB) channel pulse response between two transceivers as a source of common randomness that is not available to enemy observers in other locations. The maximum size of a key that can be shared in this way is characterized by the mutual information between the observations of two radios, and an approximation and upper bound on mutual information is found for a general multipath channel and examples given for UWB channel models. The exchange of some information between the parties is necessary to achieve these bounds, and various information-sharing strategies are considered and their performance is simulated. A qualitative assessment of the vulnerability of such a secret sharing system to attack from a radio in a nearby location is also given.

In slow-fading scenarios, cooperation between nodes can increase the amount of diversity for communication. We study the performance limit in such scenarios by analyzing the outage capacity of slow fading relay channels. Our focus is on the low signal-to-noise ratio (SNR) and low outage probability regime, where the adverse impact of fading is greatest but so are the potential gains from cooperation. We showed that while the standard Amplify-Forward protocol performs very poorly in this regime, a modified version we called the Bursty Amplify-Forward protocol is optimal and achieves the outage capacity of the network. Moreover, this performance can be achieved without a priori channel knowledge at the receivers. In contrast, the Decode-Forward protocol is strictly suboptimal in this regime. Our results directly yield the outage capacity per unit energy of fading relay channels

An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that randomly scattered nodes can achieve, with high probability, the same 1/radicn transmission rate of arbitrarily located nodes. This contrasts with previous results suggesting that a 1/radicnlogn reduced rate is the price to pay for the randomness due to the location of the nodes. The network operation strategy to achieve the result corresponds to the transition region between order and disorder of an underlying percolation model. If nodes are allowed to transmit over large distances, then paths of connected nodes that cross the entire network area can be easily found, but these generate excessive interference. If nodes transmit over short distances, then such crossing paths do not exist. Percolation theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate is then obtained by performing pairwise coding and decoding at each hop along the paths, and using a time division multiple access scheme

n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r-alphaas well as a random phase. We identify the scaling laws of the information-theoretic capacity of the network when nodes can relay information for each other. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n2/3of Aeron and Saligrama. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n2-alpha/2for 2lesalpha4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed multiple-input multiple-output (MIMO) communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.

Channel uncertainty limits the achievable data rates of certain ultra-wideband systems due to the need to estimate the channel. The use of bursty duty-cycled transmission reduces the channel uncertainty because the receiver has to estimate the channel only when transmission takes place, but the maximum amount of burstiness and hence the possible reduction of channel uncertainty both depend on the spectral efficiency of the modulation scheme used. This general principle is demonstrated by comparing the channel conditions that allow duty-cycled direct-sequence spread spectrum (DSSS) and pulse position modulation (PPM) to achieve the additive white Gaussian noise (AWGN) channel capacity in the wideband limit. We show that duty-cycled DSSS systems achieve the wideband capacity as long as the number of independently faded resolvable paths increasessublinearlywith the bandwidth, while duty-cycled PPM systems can achieve the wideband capacity only if the number of paths increasessublogarithmically. The difference is due to the fact that DSSS is spectrally more efficient than PPM and hence allows more bursty transmission.

Channel capacity in the limit of vanishing signal-to-noise ratio (SNR) per degree of freedom is known to be linear in SNR for fading and nonfading channels, regardless of channel state information at the receiver (CSIR). It has recently been shown that the significant engineering difference between the coherent and the noncoherent fading channels, including the requirement of peaky signaling and the resulting spectral efficiency, is determined by how the capacity limit is approached as SNR tends to zero, or in other words, the sublinear term in the capacity expression. In this paper, we show that this sublinear term is determined by the channel coherence level, which we define to quantify the relation between the SNR and the channel coherence time. This allows us to trace a continuum between the case with perfect CSIR and the case with no CSIR at all. Using this approach, we also evaluate the performance of suboptimal training schemes.

Diversity embedded codes are opportunistic codes which take advantage of good channel realizations while ensuring at least part of the information is received reliably for bad channels. We establish a connection between these codes and degraded message set broadcast codes. We characterize the achievable rate region for the parallel Gaussian degraded message set broadcast problem, when only the strongest user needs the private information. Using this, we partially characterize the set of achievable rate-diversity tuples for the diversity embedded problem for parallel fading channels.

We consider the CDMA (code-division multiple-access) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse signatures, and a detection algorithm based on belief propagation (BP) with linear time complexity. In the new scheme, each user conveys its power onto a finite number of chips l̄, in the large system limit. We analyze the performances of BP detection and prove that they coincide with the ones of optimal (symbol MAP) detection in the l̄ → ∞ limit. In the same limit, we prove that the information capacity of the system converges to Tanaka's formula for random 'dense' signatures, thus providing the first rigorous justification of this formula. Apart from being computationally convenient, the new scheme allows for optimization in close analogy with irregular low density parity check code ensembles.

This paper studies the feasibility and algorithms for inferring the delay at each link in a communication network based on a large number of end-to-end measurements. The restriction is that we are not allowed to measure directly on each link and can only observe the route delays. It is assumed that we have considerable flexibility in choosing which routes to measure. We investigate two different cases: 1) each link delay is a constant and 2) each link delay is modeled as a random variable from a family of distributions with unknown parameters. We will answer whether such indirect inference is possible at all, and when possible, how it can be carried out. The emphasis is on developing the maximum-likelihood estimators for scenario 2) when the link delays are modeled by exponential random variables or mixtures of exponentials. We have derived solutions based on the EM algorithm and demonstrated that, even though they do not necessarily reflect the true model parameters, they do seem to maximize the likelihood in most cases and that the resulting probability density functions match the true functions on regions where the probability mass concentrates

Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.

The impact of scattering condition and array configuration on performances are inseparable in early analyses of multiple-antenna systems. An array-independent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic property of the scattering channel itself. For linear arrays of length L in an environment of total angle spread |Omega|, the ergodic capacity is shown to increase linearly with L|Omega| for large arrays. When antenna arrays reduce to practical sizes, the capacity scaling depends on the signal-to-noise ratio (SNR) as well. This implies that the number of antennas used should also depend on the SNR. In terms of outage capacity, the tradeoff between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms. Finally, as |Omega| varies with the propagation range, the tradeoff among multiplexing gain, diversity gain, and propagation range is studied

In this paper we analyze the outage performance of a slow fading relay channel in the low SNR regime. We present a scheme, called bursty amplify and forward, which achieves the epsi-outage capacity of the relay channel for small outage probabilities epsi, and we give a simple characterization of the outage capacity. Our results directly yield the epsi-outage capacity per unit energy of the channel

Diversity-embedded codes for fading channels are high-rate codes that are designed so that they have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the information is received reliably. This can also be thought as coding the data into two streams such that the high-priority stream has higher reliability than the low-priority stream. For SISO (single-input-single-output), SIMO, MISO and parallel fading channels, we characterize the achievable rates and reliability of the two streams in the high SNR regime in terms of the diversity-multiplexing tradeoff. We exhibit the performance gain over a single-stream code. We also show some constructions for finite block lengths that achieve the optimal performance

We study the capacity of ad hoc wireless networks with mobile nodes. The mobility model examined is one where the nodes are restricted to move along one-dimensional paths. We examine the scaling laws for the per user throughput achievable over long time-scales, making this suitable for applications with loose delay constraints. We show that under this regime of restricted mobility, we attain a constant throughput (i.e., Θ (1)) per user, which is significantly higher than the throughput of fixed networks, which decays as O(1/√n) with the number of nodes n, as shown by Gupta and Kumar.

Multiple-antenna systems that are limited by the area and geometry of antenna arrays, are considered. Given these physical constraints, the limit on the available number of spatial degrees of freedom is derived. The commonly used statistical multiple-input multiple-output (MIMO) model is inadequate. Antenna theory is applied to take into account the area and geometry constraints, and to define the spatial signal space so as to interpret experimental channel measurements in an array-independent but manageable description of the physical environment. Based on these modeling strategies, for a spherical array of effective aperture A in a physical environment of angular spread |/spl Omega/| in solid angle, the number of spatial degrees of freedom is shown to be A|/spl Omega/| for uni-polarized antennas and 2A|/spl Omega/| for tri-polarized antennas. Together with the 2WT degrees of freedom for a system of bandwidth W transmitting in an interval T, the total degrees of freedom of a multiple-antenna channel is therefore 4WTA|/spl Omega/|.

We consider the problem of how throughput in a wireless network with randomly located nodes scales as the number of users grows. Following the physical model of Gupta and Kumar, we show that randomly scattered nodes can achieve the optimal 1/(n)/sup 1/2/ per-node transmission rate of arbitrarily located nodes. This contrasts with previous achievable results suggesting that a 1/(n log n)/sup 1/2/ reduced rate is the price to pay for the additional randomness introduced into the system. Our results rely on percolation theory arguments. In the high density regime the network is fully connected but generates excessive interference. In the low density regime the network loses connectivity. Percolation theory ensures that a wireless backbone forms in the transition region between this two extreme scalings. This backbone does not cover all the nodes, nevertheless it is sufficiently rich in crossing paths so that it can transport all the traffic in the network. By operating the network in this transition region between order and disorder, we are able to prove our tight bound.

This paper computes the optimal diversity multiplexing curve for intersymbol interference (ISI) channels and reveal it equals the matched filter bound. A simple transmission scheme that achieves this bound is presented and analyzed. The scheme provides a tractable method of extracting maximal diversity gain for any spatial multiplexing gain, when communicating over multipath fading channels.

In the so-called CEO problem, a hidden source random process is of interest to a central unit or the "CEO". But this process cannot be observed directly. L sensors or agents observe independently corrupted versions of the source. They encode their observations without cooperating with one another and send through rate constrained noiseless channels to the CEO. The problem was first studied by T. Berger et al. (1996) in the context of discrete memoryless sources. The quadratic Gaussian version of the problem was studied. The best result known to date is the characterization of the sum-rate when all the agents have the same quality of observations. Here we characterize the rate region for any number of agents without assuming that their quality of observations is the same. This is one of the few examples of multiterminal lossy source coding problems in which the rate region can be characterized completely.

The effect of channel coherence on the capacity and energy efficiency of noncoherent fading channels at low SNR is studied. A simple characterization is given, and a new approach is developed, which can be used to study a wide variety of problems for communications over a wideband channel. The flat block fading channel is studied, which transmits one scalar symbol per symbol time distorted by a multiplicative fading coefficient and the additive Gaussian noise.

We study the capacity of fading channels with no CSI at both the transmitter and the receiver. We focus on the low SNR regime, and study the impact of channel memory on the capacity. While the current results on these issues are based on various limiting assumptions, we use a new approach of asymptotic analysis to capture the relation among the key system parameters, and depict the continuum between the extreme cases.

We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols.

In a point-to-point wireless fading channel, multiple transmit and receive antennas can be used to improve the reliability of reception (diversity gain) or increase the rate of communication for a fixed reliability level (multiplexing gain). In a multiple-access situation, multiple receive antennas can also be used to spatially separate signals from different users (multiple-access gain). Recent work has characterized the fundamental tradeoff between diversity and multiplexing gains in the point-to-point scenario. In this paper, we extend the results to a multiple-access fading channel. Our results characterize the fundamental tradeoff between the three types of gain and provide insights on the capabilities of multiple antennas in a network context.

This paper develops a physical channel model for multiple-antenna systems. The model appropriately abstracts the scattering intensity of physical environments, geometry of antenna arrays and degrees of polarization. Then, we use the model to demonstrate that the "space" in wireless systems is composed of three signal dimensions: wavevector, array and polarization. The impact of physical environment, array geometry and polarization are captured separately in the wavevector, array and polarization dimensions respectively. Thus, we solidify the "space" dimensions in complement to the time and frequency dimensions, and unify the available signal space in wireless channels.

Protocols such as TCP require packets to be accepted (i.e., delivered to the receiving application) in the order they are transmitted at the sender. Packets are sometimes mis-ordered in the network. In order to deliver the arrived packets to the application in sequence, the receiver's transport layer needs to temporarily buffer out-of-order packets and resequence them as more packets arrive. Even when the application can consume the packets infinitely fast, the packets may still be delayed for resequencing. In this paper, we model packet mis-ordering by adding an IID random propagation delay to each packet and analyze the required buffer size for packet resequencing and the resequencing delay for an average packet. We demonstrate that these two quantities can be significant and show how they scale with the network bandwidth.

The paper proposes an adaptive multiantenna transceiver for narrowband reception. Blind channel tracking algorithms are developed to track the eigen directions of the channel directly instead of the channel itself. Two algorithms are proposed to track the column space of the channel at the receiver, based on the received data. One of the algorithms is free of any division operation, which is more favorable in practice. For the row space of the channel, two approaches are proposed as well. The first approach requires periodic feedback of the demodulated signal from the receiver back to the transmitter where it can make use of its knowledge on the prior transmitted symbols to estimate the row space. In the second approach, the estimation is done at the receiver based on the detected symbols, and the estimated row space is sent back to the transmitter. Adaptive resource allocation is also incorporated into the design.

We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate four-way connection between the vector broadcast channel, the corresponding point-to-point channel (where the receivers can cooperate), the multiple-access channel (MAC) (where the role of transmitters and receivers are reversed), and the corresponding point-to-point channel (where the transmitters can cooperate).

Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.

We propose a time-scale decomposition approach to measurement-based admission control (MBAC). We identify a critical time scale, T/spl tilde//sub h/, such that: 1) aggregate traffic fluctuations slower than T/spl tilde//sub h/ can be tracked by the admission controller and compensated for by flow admissions and departures; 2) fluctuations faster than T/spl tilde//sub h/ have to be absorbed by reserving spare bandwidth on the link. The critical time scale is shown to scale as T/sub h///spl radic/n, where T/sub h/ is the average flow duration and n is the size of the link in terms of the number of flows it can carry. An MBAC design is presented which filters aggregate measurements into low- and high-frequency components separated at the cutoff frequency, 1/T/spl tilde//sub h/, using the low-frequency component to track slow time-scale traffic fluctuations and the high-frequency component to estimate the spare bandwidth needed. Our analysis shows that the scheme achieves high utilization and is robust to traffic heterogeneity, multiple time-scale fluctuations and measurement errors. The scheme uses only measurements of aggregate bandwidth and does not need to keep track of per-flow information.

Previous studies have shown that single-user systems employing n-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n, assuming independent Rayleigh fading between antenna pairs. We explore the capacity of dual-antenna-array systems under correlated fading via theoretical analysis and ray-tracing simulations. We derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases; the latter is derived under some assumptions about the scaling of the fading correlation structure. In both cases, the theoretic capacity growth is linear in n but the growth rate is 10-20% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model. Results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n = 16. We present results for both the cases when the transmitter does and does not know the channel realization.

Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent time-varying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak. The diversity gain increases with the dynamic range of the fluctuations and is thus limited in environments with little scattering and/or slow fading. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. The scheme can be interpreted as opportunistic beamforming and we show that true beamforming gains can be achieved when there are sufficient users, even though very limited channel feedback is needed. Furthermore, in a cellular system, the scheme plays an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing. this scheme in a complete wireless system.

We study the capacity of multiple-antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald (see ibid. vol.45, p.139-57, 1999). The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length T symbol periods. We compute the asymptotic capacity of this channel at high signal-to-noise ratio (SNR) in terms of the coherence time T, the number of transmit antennas M, and the number of receive antennas N. While the capacity gain of the coherent multiple antenna channel is min{M, N} bits per second per Hertz for every 3-dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be M* (1 - M*/T) bits per second per Hertz, where M*=min{M, N, [T/2]}. The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold.

The capacity of ad hoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an ad hoc network where n nodes communicate in random source-destination pairs. These nodes are assumed to be mobile. We examine the per-session throughput for applications with loose delay constraints, such that the topology changes over the time-scale of packet delivery. Under this assumption, the per-user throughput can increase dramatically when nodes are mobile rather than fixed. This improvement can be achieved by exploiting a form of multiuser diversity via packet relaying.

The capacity of ad-hoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an ad-hoc network where n nodes communicate in random source-destination pairs. These nodes are assumed to be mobile. We examine the per-session throughput for applications with loose delay constraints, such that the topology changes over the time-scale of packet delivery. Under this assumption, the per-user throughput can increase dramatically when the nodes are mobile rather than fixed. This improvement can be achieved by exploiting node mobility as a type of multiuser diversity.

Much of the performance analysis on multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems is focused on worst case near-far scenarios. The user capacity of power-controlled networks with multiuser receivers are less well-understood. Tse and Hanly (see ibid., vol.45, p.541-657, 1999) have shown that under some conditions, the user capacity of an uplink power-controlled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. We show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signal-to-interference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.

Dynamic resource allocation is an important means to increase the sum capacity of fading multiple-access channels (MACs). In this paper, we consider vector multi-access channels (channels where each user has multiple degrees of freedom) and study the effect of power allocation as a function of the channel state on the sum capacity (or spectral efficiency) defined as the maximum sum of rates of users per unit degree of freedom at which the users can jointly transmit reliably, in an information-theoretic sense, assuming random directions of received signal. Direct-sequence code-division multiple-access (DS-CDMA) channels and MACs with multiple antennas at the receiver are two systems that fall under the model. Our main result is the identification of a simple dynamic power-allocation scheme that is optimal in a large system, i.e., with a large number of users and a correspondingly large number of degrees of freedom. A key feature of this policy is that, for any user, it depends on the instantaneous amplitude of channel state of that user alone and the structure of the policy is "water-filling." In the contest of DS-CDMA and in the special case of no fading, the asymptotically optimal power policy of water-filling simplifies to constant power allocation over all realizations of signature sequences; this result verifies the conjecture made in Verdu and Shamai (1999). We study the behavior of the asymptotically optimal water-filling policy in various regimes of number of users per unit degree of freedom and signal-to-noise ratio (SNR). We also generalize this result to multiple classes, i.e., the situation when users in different classes have different average power constraints.

Multiple-access interference (MAI) in a code-division multiple-access (CDMA) system plays an important role in performance analysis and characterization of fundamental system limits. We study the behavior of the output MAI of the minimum mean-square error (MMSE) receiver employed in the uplink of a direct-sequence (DS)-CDMA system. We focus on imperfect power-controlled systems with random spreading, and establish that in a synchronous system (1) the output MAI of the MMSE receiver is asymptotically Gaussian, and (2) for almost every realization of the signatures and received powers, the conditional distribution of the output MAI converges weakly to the same Gaussian distribution as in the unconditional case. We also extend our study to asynchronous systems and establish the Gaussian nature of the output interference. These results indicate that in a large system the output interference is approximately Gaussian, and the performance of the MMSE receiver is robust to the randomness of the signatures and received powers. The Gaussianity justifies the use of single-user Gaussian codes for CDMA systems with linear MMSE receivers, and implies that from the viewpoints of detection and channel capacity, signal-to-interference ratio (SIR) is the key parameter that governs the performance of the MMSE receiver in a CDMA system.

Wireless systems using multi-element antenna arrays simultaneously at the both transmitter and receiver promise a much higher capacity than conventional systems. Previous studies have shown that single-user systems employing n-element transmit and receive arrays can achieve a capacity proportional to n, assuming independent Rayleigh fading between pairs of antenna elements. We explore the capacity of dual-antenna-array systems via theoretical analysis and simulation experiments. We present expressions for the asymptotic growth rate of capacity with n for both independent and correlated fading cases; the latter is derived under some assumptions about the fading correlation structure. We show that the capacity growth is linear in n in both the independent and correlated cases, but the growth rate is smaller in the latter case. We compare the predictions of our asymptotic theory to the capacities of channels simulated using ray tracing, and find good agreement even for moderate n, i.e., 1/spl les/n/spl les/16. Our results address both the cases when the transmitter does and does not know the channel realization.

In this paper, we study the capacity of multiple antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a block fading model proposed by Marzetta and Hochwald (see IEEE Trans. on Info. Theory, vol.45, no.1, p.139-57, 1999). The model does not assume any prior knowledge of the fading coefficients, but only assumes that the coefficients remain constant for a coherent interval T as an approximation of the continuously varying channel. We compute the asymptotic capacity of this channel at high SNR in terms of T, the number of transmit antennas M and the number of receive antennas N. While the capacity gain of the coherent multi-antenna channel is min{M,N} bps/Hz for every 3 dB increase in SNR, the corresponding gain for the non-coherent channel turns out to be M/sup */(1-M/sup *//T) bps/Hz, where M/sup */=min{M,N,[T/2]}. The capacity expression has a geometric interpretation of sphere packing in the Grassmann manifold.

A linear multiuser receiver for a particular user in a code-division multiple-access (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. We study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signal-to-interference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signal-to-interference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference.

The performance of linear multiuser receivers in terms of the signal-to-interference ratio (SIR) achieved by the users has been analyzed in a synchronous CDMA system under random spreading sequences. In this paper, we extend these results to a symbol-asynchronous but chip-synchronous system and characterize the SIR for linear receivers-the matched-filter receiver the minimum mean-square error (MMSE) receiver and the decorrelator. For each of the receivers, we characterize the limiting SIR achieved when the processing gain is large and also derive lower bounds on the SIR using the notion of effective interference. Applying the results to a power controlled system, we derive effective bandwidths of the users for these linear receivers and characterize the user capacity region: a set of users is supportable by a system if the sum of the effective bandwidths is less than the processing gain of the system. We show that while the effective bandwidth of the decorrelator and the MMSE receiver is higher in an asynchronous system than that in a synchronous system, it progressively decreases with the increase in the length of the observation window and is asymptotic to that of the synchronous system, when the observation window extends infinitely on both sides of the symbol of interest. Moreover, the performance gap between the MMSE receiver and the decorrelator is significantly wider in the asynchronous setting as compared to the synchronous case.

We investigate the capacity and mutual information of a broadband fading channel consisting of a finite number of time-varying paths. We show that the capacity of the channel in the wideband limit is the same as that of a wideband Gaussian channel with the same average received power. However, the input signals needed to achieve the capacity must be "peaky" in time or frequency. In particular, we show that if white-like signals are used instead (as is common in spread-spectrum systems), the mutual information is inversely proportional to the number of resolvable paths L/spl tilde/ with energy spread out, and in fact approaches 0 as the number of paths gets large. This is true even when the paths are assumed to be tracked perfectly at the receiver. A critical parameter L/spl tilde//sub crit/ is defined in terms of system parameters to delineate the threshold on L over which such overspreading phenomenon occurs.

This correspondence analyzes the high signal-to-noise ratio (SNR) performance of optimum multiuser detectors for synchronous direct-sequence spread spectrum with random spreading in an additive white Gaussian noise channel. Under very general conditions on the received powers, we show that the optimum asymptotic efficiency of a K-user system with spreading gain N converges to 1 almost surely as K/spl rarr//spl infin/, and K/N is kept equal to an arbitrary nonzero constant. Therefore, the asymptotic behavior of the minimum bit error rate is equivalent to that of a single-user system.

We study the signal-to-interference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions." Such a random environment may arise in a DS-CDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the receiver, the resulting SIR performance is a function of the directions and therefore also random. We study the asymptotic distribution of this random performance in the regime where both the number of users K and the number of degrees of freedom N in the system are large, but keeping their ratio fixed. Our results show that for both the decorrelator and the minimum mean-square error (MMSE) receiver, the variance of the SIR distribution decreases like 1/N, and the SIR distribution is asymptotically Gaussian. We compute closed-form expressions for the asymptotic means and variances for both receivers. Simulation results are presented to verify the accuracy of the asymptotic results for finite-sized systems.

Multimedia traffic sources with tight latency constraint, arising in sessions such as data query, image and video transmissions, can be very bursty and are inefficient to be serviced with a dedicated high-speed link. On wireline networks, bursty traffic is statistically multiplexed to fully utilize the link capacity. In light of recent proposals for wideband CDMA (WCDMA) to service multimedia data, there is a similar need to develop wireless network architectures with flexible bandwidth allocation to facilitate statistical multiplexing. To address this issue, we compared the throughput performance of two promising WCDMA configurations, high speed CDMA (HS-CDMA) and multi-code CDMA (MC-CDMA). HS-CDMA assigns each user a single code with small spreading gain to enable a high transmission rate when it is needed. In contrast, MC-CDMA employs codes with a large spreading gain but permits a user to acquire more than one code. As expected, the throughput of a configuration depends on the receiver structure as well as the operation scenarios like power and SNR constraints. When matched filter receivers are applied, HS-CDMA fares better in most occasions. When multi-user receivers are used, both configurations deliver the same throughput except the situation when the total power is bounded.

We propose a time-scale decomposition approach to measurement-based admission control (MBAC). We identify a critical time-scale T/spl tilde//sub h/ such that: (1) aggregate traffic fluctuation slower than T/spl tilde//sub h/ can be tracked by the admission controller and compensated for by flow admissions and departures; (2) fluctuations faster than T/spl tilde//sub h/ have to be absorbed by reserving spare bandwidth on the link. The critical time-scale is shown to scale as T/sub h///spl radic/n, where T/sub h/ is the average flow duration and n is the size of the link in terms of number of flows it can carry. A MBAC design is presented which filters aggregate measurements into low and high frequency components separated at the cutoff frequency 1/T/spl tilde//sub h/, using the low frequency component to track slow time-scale traffic fluctuations and the high frequency component to estimate the spare bandwidth needed. The analysis shows that the scheme achieves high utilization and is robust to traffic heterogeneity, multiple time-scale fluctuations and measurement errors. The scheme uses only measurements of aggregate bandwidth and does not need to keep track of per-flow information.

The performance and computational complexity of five multi-access receivers are compared. A methodology is then presented for making area and power estimates of these algorithms for both software programmable DSP and dedicated direct mapped architectures. With this methodology and by using experimental data from previous designs, the feasibility of implementation of the multi-access receivers can be determined.

Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. We show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison.

There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spread-spectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (S-CDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its quality-of-service (QoS) requirement (expressed in terms of its desired signal-to-interference ratio) met. This characterization allows one to describe the user capacity through a simple effective bandwidth characterization: users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity.

Measurement-based admission control (MBAC) is an attractive mechanism to concurrently offer quality of service (QoS) to users, without requiring a priori traffic specification and on-line policing. However, several aspects of such a system need to be dearly understood in order to devise robust MBAC schemes, i.e., schemes that can match a given QoS target despite the inherent measurement uncertainty, and without the tuning of external system parameters. We study the impact of measurement uncertainty, flow arrival, departure dynamics, and of estimation memory on the performance of a generic MBAC system in a common analytical framework. We show that a certainty equivalence assumption, i.e., assuming that the measured parameters are the real ones, can grossly compromise the target performance of the system. We quantify the improvement in performance as a function of the length of the estimation window and an adjustment of the target QoS. We demonstrate the existence of a critical time scale over which the impact of admission decisions persists. Our results yield new insights into the performance of MBAC schemes, and represent quantitative and qualitative guidelines for the design of robust schemes.

To meet the increasing capacity demand on wireless networks there have been intense efforts in the past decade on developing multiuser receiver structures which mitigate the interference between users in spread-spectrum and antenna array systems. While much of the research is performed at the physical layer, the capacity of networks with multiuser receivers and the associated resource allocation problems are less well-understood. We show that under some conditions, the capacity of a single cell for several important receivers can be very simply characterized via a notion of effective bandwidth: the QoS requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The number of degrees of freedom is the processing gain in a spread-spectrum system and the number of antenna elements in an antenna array. The effective bandwidth of a user depends only on its own QoS requirement, expressed in terms of the desired signal-to-interference ratio. It is hoped that such an abstraction of resource requirement will help in bridging the resource allocation problems at the networking layer and multiuser techniques at the physical layer.

For pt.I see ibid., vol.44, no.7, p.2796-815 (1998). In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. In the present paper, we introduce a notion of delay-limited capacity which is the maximum rate achievable with delay independent of how slow the fading is. We characterize the delay-limited capacity region of the multiaccess fading channel and the associated optimal resource allocation schemes. We show that successive decoding is optimal, and the optimal decoding order and power allocation can be found explicitly as a function of the fading states; this is a consequence of an underlying polymatroid structure that we exploit.

In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. We characterize the throughput capacity region which contains the long-term achievable rates through the time-varying channel. We show that each point on the boundary of the region can be achieved by successive decoding. Moreover, the optimal rate and power allocations in each fading state can be explicitly obtained in a greedy manner. The solution can be viewed as the generalization of the water-filling construction for single-user channels to multiaccess channels with arbitrary number of users, and exploits the underlying polymatroid structure of the capacity region.

We consider the problem of admission control for variable-rate traffic sources sharing a bufferless link, in order to provide a quality-of-service in terms of overload probability. Through analysis and simulations, we study the performance of a scheme which has no prior knowledge of the traffic statistics and makes admission decision based on the current network state only. We analyze the dynamics of the system under this control, and show that in the regime of large link capacity and separation of call and burst time-scales, this scheme performs as well as the optimal scheme which has full knowledge of the statistics. We evaluate the performance of the scheme on real traffic sources.

Measurement-based Admission Control (MBAC) is an attractive mechanism to concurrently offer Quality of Service (QoS) to users, without requiring a-priori traffic specification and on-line policing. However, several aspects of such a system need to be clearly understood in order to devise robust MBAC schemes. Through a sequence of increasingly sophisticated stochastic models, we study the impact of parameter estimation errors, of flow arrival and departure dynamics, and of estimation memory on the performance of an MBAC system.We show that a certainty equivalence assumption, i.e., assuming that the measured parameters are the real ones, can grossly compromise the target performance of the system. We quantify the improvement in performance as a function of the memory size of the estimator and a more conservative choice of the certainty-equivalent parameters. Our results yield valuable new insight into the performance of MBAC schemes, and represent quantitative guidelines for the design of robust schemes.

Variable bit-rate (VBR) compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage because it has strict delay and loss requirements while simultaneously exhibiting burstiness at multiple time scales. We show that burstiness over long time scales, in conjunction with resource reservation using one-shot traffic descriptors, can substantially degrade the loss rate, end-to-end delay, and statistical multiplexing gain of a connection. We use large-deviation theory to model the performance of multiple time-scale traffic and to motivate the design of renegotiated constant bit rate (RCBR) service. Sources using RCBR service are presented with an abstraction of a fixed-size buffer which is drained at a constant rate. They may renegotiate the drain rate to match their workload. Because all traffic entering the network is constant bit-rate (CBR), RCBR requires minimal buffering and scheduling support in switches. We show that the service is suitable for both stored and online video sources. An RCBR source must decide when to renegotiate its service rate and what the new service rate should be. We present: (1) an algorithm to compute the optimal renegotiation schedule for stored (offline) traffic and (2) a heuristic to approximate the optimal schedule for online traffic. We also discuss measurement-based admission control (MBAC) for RCBR traffic. Simulation experiments show that RCBR is able to extract almost all of the statistical multiplexing gain available by exploiting slow time-scale variations in traffic. Moreover, simple admission control schemes are sufficient to keep the renegotiation failure probability below a small threshold while still offering high link utilization. Thus, we believe that RCBR is a simple, practical, and effective service for carrying multiple time-scale traffic.

Compressed video traffic is expected to be a significant component of the traffic mix in integrated services networks. This traffic is hard to manage, since it has strict delay and loss requirements, but at the same time, exhibits burstiness at multiple time-scales. In this paper, we observe that slow time-scale variations can cause sustained peaks in the source rate, substantially degrading performance. We use large deviation theory to study this problem and to motivate the design of Renegotiated Constant Bit Rate Service (RCBR), that adds renegotiation and buffer monitoring to traditional CBR service. We argue the the load placed on signalling by RCBR can be handled by current technology. We present a) an algorithm to compute the optimal renegotiation schedule for stored (off-line) traffic, and b) a heuristic to approximate the optimal schedule for online traffic. Simulation experiments show that RCBR is able to extract almost all of the statistical multiplexing gain available by exploiting slow time-scale variations in traffic. In more general terms, we believe that a clean system design must match control time-scales to the time scales over which the workload varies. RCBR works well because it makes intelligent use of this time-scale separation.

We study the problem of statistical multiplexing of cell streams that have correlations at multiple time-scales. Each stream is modeled by a singularly perturbed Markov-modulated process with some state transitions occurring much less frequently than others. One motivation of this model comes from variable-rate compressed video, where the fast time-scale dynamics may correspond to correlations between adjacent frames, while the slow time-scale dynamics may correspond to correlations which in the same scene of a video sequence. We develop a set of large deviations results to estimate the buffer overflow probabilities in various asymptotic regimes in the buffer size, rare transition probabilities, and the number of streams. Using these results, we characterize the multiplexing gain in both the channel capacity and the buffering requirements and highlight the impact of the slow time-scale of the streams.>

The following problem arises in many applications involving classification, identification, and inference. There is a set of objects X, and a particular x /spl isin/ X is chosen (unknown to us). Based on information obtained about x in a sequential manner, one wishes to decide whether x belongs to one class of objects A/sub 0/ or a different class of objects A/sub 1/. The authors study a general paradigm applicable to a broad range of problems of this type, which they refer to as problems of class identification or discernibility. They consider various types of information sequences, and various success criteria including discernibility in the limit, discernibility with a stopping criterion, uniform discernibility, and discernibility in the Cesaro sense. They consider decision rules both with and without memory. Necessary and sufficient conditions for discernibility are provided for each case in terms of separability conditions on the sets A/sub 0/ and A/sub 1/. They then show that for any sets A/sub 0/ and A/sub 1/, various types of separability can be achieved by allowing failure on appropriate sets of small measure. Applications to problems in language identification, system identification, and discrete geometry are discussed.>