Neural compression has brought tremendous progress in designing lossy compressors with good rate-distortion (RD) performance at low complexity. Thus far, neural compression design involves transforming the source to a latent vector, which is then rounded to integers and entropy coded. While this approach has been shown to be optimal on a few specific sources, we show that it can be highly sub-optimal on synthetic sources whose intrinsic dimensionality is greater than one. With integer rounding in the latent space, the quantization regions induced by neural transformations, remain square-like and fail to match those of optimal vector quantization. We demonstrate that this phenomenon is due to the choice of scalar quantization in the latent space, and not the transform design. By employing lattice quantization instead, we propose Lattice Transform Coding (LTC) and show that it approximately recovers optimal vector quantization at reasonable complexity. On real-world sources, LTC improves upon standard neural compressors. LTC also provides a framework that can integrate structurally (near) optimal information-theoretic designs into lossy compression; examples include block coding, which yields coding gain over optimal one-shot coding and approaches the asymptotically-achievable rate-distortion function, as well as nested lattice quantization for low complexity fixed-rate coding.

Group testing is traditionally considered effective only in settings with low infection rates. However, recent models that capture correlation among individuals, especially through hypergraphs, raise the question of whether group testing can remain efficient even when the infection rate is high. In this work, we study adaptive group testing under correlated settings modeled by hypergraphs and show that group testing can remain effective by leveraging these correlations to infer node states. We first state our results for k-partite hypergraphs and graphs with pairwise bounded edge intersections, and provide testing strategies that remain efficient even when the average number of infections is high. We then focus on a special class of hypergraphs called hypertrees, where infections originate from a single seed, and show that the number of tests depends on the Hamiltonian number of the underlying tree and the entropy of the edges. We then generalize the results to two seeds infection and more general contact graphs.

Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence. Theoretical work on RDP describes properties of RDP-optimal compressors without providing constructive and low complexity solutions. While classical rate-distortion theory shows that optimal compressors should efficiently pack space, RDP theory additionally shows that infinite randomness shared between the encoder and decoder may be necessary for RDP optimality. In this paper, we propose neural compressors that are low complexity and benefit from high packing efficiency through lattice coding and shared randomness through shared dithering over the lattice cells. For two important settings, namely infinite shared and zero shared randomness, we analyze the RDP tradeoff achieved by our proposed neural compressors and show optimality in both cases. Experimentally, we investigate the roles that these two components of our design, lattice coding and randomness, play in the performance of neural compressors on synthetic and real-world data. We observe that performance improves with more shared randomness and better lattice packing.

Group testing, a problem with applications in various fields, traditionally assumes independent node states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes, challenging the simplifying assumptions made in existing models. In this work, we consider a comprehensive model for arbitrary statistical correlation among node states. To capture and leverage these correlations effectively, we model the problem by hypergraphs inspired by [1]. We establish that arbitrary correlations among nodes can be represented as a hypergraph with a probability distribution over its edges, and design a novel greedy adaptive algorithm capable of conducting informative tests and dynamically updating the distribution. We analyze its performance and give theoretical guarantees on the number of tests that depend solely on the entropy of the underlying probability distribution and the average number of infections.

In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model and analyze group testing on n correlated nodes whose interactions are specified by a graph G. We model correlation through an edge-faulty random graph formed from G in which each edge is dropped with probability$1-r$, and in the newly formed graph, all nodes in the same component have the same state. We consider three classes of graphs: cycles and trees, d-regular graphs and stochastic block models or SBM, and obtain lower and upper bounds on the number of tests needed to identify the defective nodes. Roughly speaking, we use correlation among the states of the nodes to transform the problem into that of a smaller graph with independent node states. This enhancement is quantified through the ratio of the diminished node count to the overall count of nodes, n; thus, a lower ratio signifies superior performance. The lower bounds are derived by illustrating a strong dependence of the number of tests needed on the expected number of components. In this regard, we establish a new approximation for the distribution of component sizes in “d-regular trees” which may be of independent interest and leads to a lower bound on the expected number of components in d-regular graphs. The upper bounds are found by forming dense subgraphs in which nodes are more likely to be in the same state. When G is a cycle or tree, we show an improvement by a factor of$\log (1/r)$. For grid, a graph with almost$2n$edges, the improvement is by a factor of$(1-r) \log (1/r)$, indicating drastic improvement compared to trees. When G has a larger number of edges, as in SBM, the improvement can scale in n.

We discuss a federated learned compression problem, where the goal is to learn a compressor from real-world data which is scattered across clients and may be statistically heterogeneous, yet share a common underlying representation. We propose a distributed source model that encompasses both characteristics, and naturally suggests a compressor architecture that uses analysis and synthesis transforms shared by clients. Inspired by personalized federated learning methods, we employ an entropy model that is personalized to each client. This allows for a global latent space to be learned across clients, and personalized entropy models that adapt to the clients’ latent distributions. We show empirically that this strategy outperforms solely local methods, which indicates that learned compression also benefits from a shared global representation in statistically heterogeneous federated settings.

With the growth of big data in the past few decades, compression has become inseparable from data generation. The data generated daily across different platforms are correlated: friend networks on Facebook and Instagram, contact networks in subsequent days, and many more. This raises the question of compressing a dataset using another correlated dataset. For instance, can we compress the Facebook graph of friends when we know Instagram’s graph? This can be cast as the classical problem of source coding with side information, and the answer is known to be positive when the graphs are "labeled" and/or aligned, meaning we need to know the node corresponding to Jon Doe in both Facebook and Instagram graphs. The classical idea is to utilize joint typicality to decide whether two graphs are correlated or not. In practice, graphs are often not aligned and/or the labels are concealed to keep the identity of the users private. In these scenarios, classical ideas are no longer applicable as joint typicality highly depends on the ordering of sequences. In this work, we prove for the first time the existence of lossless graph compression schemes that utilize unlabeled side information and improve the compression rate. In order to do that, we design binning along with a novel testing criterion that relies on graph matching, the closely related quadratic assignment problem and its asymptotic properties.

A diamond network is considered in which the central processor is connected, via backhaul noiseless links, to multiple conferencing base stations that communicate with a single user over a multiple access channel. We propose coding techniques along with lower and upper bounds on the capacity. Our achievability scheme uses a common cloud coding strategy based on the technique proposed by Wand, Wigger, and Zaidi (2018) and extends it beyond two relays. Our upper bounds generalize the method proposed by Bidokhti and Kramer (2016) and lead to new bounds for the multiple conferencing relay setting. Specializing our upper bounds to the two relay scenario, we provide new bounds and improve the state-of-the-art.

A fundamental question in designing lossy data compression schemes is how well one can do in comparison with the rate-distortion function, which describes the known theoretical limits of lossy compression. Motivated by the empirical success of deep neural network (DNN) compressors on large, real-world data, we investigate methods to estimate the rate-distortion function on such data, which would allow comparison of DNN compressors with optimality. While one could use the empirical distribution of the data and apply the Blahut-Arimoto algorithm, this approach presents several computational challenges when the datasets are large and high-dimensional, such as the case of modern image datasets. Instead, we reformulate the rate-distortion objective, and solve the resulting functional optimization problem using neural networks. We provide experimental results on popular image datasets, and provide theoretical evidence why our method can accurately estimate the rate-distortion function. Additionally, we show that the rate-distortion achievable by DNN compressors are within several bits of the rate-distortion function. Lastly, we connect the rate-distortion objective and entropic optimal transport, and describe a method to implement an operational lossy compression scheme with guarantees on the achievable rate and distortion.

In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model and analyze group testing on n correlated nodes whose interactions are specified by a graph G. We model correlation through an edge-faulty random graph formed from G in which each edge is dropped with probability 1−r, and all nodes in the same component have the same state.We consider three classes of graphs: cycles and trees, d-regular graphs, and stochastic block models or SBM, and obtain lower and upper bounds on the number of tests needed to identify the defective nodes. Our results are expressed in terms of the number of tests needed when the nodes are independent and they are in terms of n, r, and the target error. In particular, we quantify the fundamental improvements that exploiting correlation offers by the ratio between the total number of nodes n and the equivalent number of independent nodes in a classic group testing algorithm.The lower bounds are derived by illustrating a strong dependence of the number of tests needed on the expected number of components. In this regard, we establish a new approximation for the distribution of component sizes in "d-regular trees" which may be of independent interest and leads to a lower bound on the expected number of components in d-regular graphs.The upper bounds are found by forming dense subgraphs in which nodes are more likely to be in the same state. When G is a cycle or tree, we show an improvement by a factor of log(1/r). For grid, a graph with almost 2n edges, the improvement is by a factor of (1 − r)log(1/r), indicating drastic improvement compared to trees. When G has a larger number of edges, as in SBM, the improvement can scale in n.

In applications of remote sensing, estimation, and control, timely communication is critical but not always ensured by high-rate communication. This work proposes decentralized age-efficient transmission policies for random access channels with$M$transmitters. We propose the notion ofage-gainof a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a decentralized manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large$M$, we prove that when the arrival rate is small (below$\frac {1}{eM}$), slotted ALOHA-type algorithms are order optimal. As the arrival rate increases beyond$\frac {1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates$\theta $,$\theta =\frac {1}{o(M)}$, the proposed algorithms provide a multiplicative gain of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain. This is surprising and contrary to common practice where the arrival rate is optimized to attain the minimum AoI. We further extend our results to other random access technologies such as Carrier-sense multiple access (CSMA).

Real-time sampling and estimation of autoregressive Markov processes is considered in random access channels. Two classes of policies are studied: (i) oblivious policies in which decision making is independent of the source realizations, and (ii) non-oblivious policies in which sources are observed causally for decision making. In the first class, minimizing the expected time-average estimation error is equivalent to minimizing the expected age of information (AoI). Lower and upper bounds are provided for the achievable estimation error in this class and age-based threshold policies are shown to provide a two-fold improvement compared to the state-of-the-art. In the second class, an error-based threshold policy is proposed: a transmitter becomes active when its error exceeds a threshold in which case it transmits probabilistically following slotted ALOHA. A closed-form expression is derived for the estimation error as a function of the peak age, the transmission delay, a term which we call the silence delay, as well as the source realization. It is analyzed approximately by considering the underlying source as a discretized Wiener process. The proposed threshold policy provides a three-fold improvement compared to oblivious policies and its performance is close to that of centralized greedy scheduling.

Timeliness of information transfer is critical in real-time applications. Prioritizing timeliness, however, often comes at the cost of rate inefficiency, especially in block coding. In this work, motivated by the sequential nature of encoding and decoding in arithmetic source coding, the timeliness of arithmetic coding is investigated. For a generate-at-will source model, an upper bound is provided on the average peak age of information (PAoI). This upper bound builds on the arithmetic coding scheme of Shayevitz et al. (2007) which has a finite look-ahead parameter$d$. It captures interesting trade-offs between PAoI, compression rate, and the look-ahead parameter$d$. For periodic sources, rate efficiency is argued to be less critical than the look-ahead parameter$d$in minimizing the peak age, especially when the traffic load is moderate and small. Through simulations, two observations are made: (i) the optimal look-ahead parameter$d$is an increasing function of the traffic load, and (ii) asymptotically, as the traffic load gets close to its limit 1, the classical arithmetic coding (without a finite bound on$d$) performs better than the state-of-the-art age-optimal block codes.

The interplay between timeliness and rate efficiency is investigated in packet erasure broadcast channels with feedback. A scheduling framework is proposed in which coding actions, as opposed to users, are scheduled to attain desired tradeoffs between rate and age of information (AoI). This tradeoff is formalized by an upper bound on AoI as a function of the target rate constraints and two lower bounds: one as a function of the communication rate and one as a function of the arrival rate. Simulation results show that (i) surprisingly, coding can be beneficial in reducing AoI in the regime of moderate arrival rates even without rate constraints and the benefit increases with the number of users, and (ii) AoI increases with both the target rate constraint and the arrival rate when either is kept fixed, but decreases with them when they are set to be equal.

In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. Oftentimes, it is observed that as the capacity of a system is approached, delay increases significantly and so does age of information - a metric recently proposed to capture freshness and timeliness of information. This work proposes decentralized age-efficient transmission policies for random access channels with M transmitters and provides asymptotic results for the age of information as M → ∞. Slotted ALOHA-type algorithms are shown to be asymptotically age-optimal for arrival rates below 1/eM and far from optimal for larger arrival rates. For larger arrival rates, novel decentralized age-based policies are proposed that benefit from the availability of fresh packets to reduce age of information. For arrival rates θ, θ = 1/o(M)1, the proposed algorithms provide a multiplicative gain factor of at least two compared to the state-of-the-art schemes. We conclude that it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their “age-gains”, a notion defined in the paper. This is surprising and contrary to common practice where the arrival rate is optimized to attain the minimum AoI.

Coding for random access communication is a key challenge in Internet of Things applications. In this paper, the well-known scheme of Coded Slotted Aloha (CSA) is considered and its performance is analyzed in the non-asymptotic regime where the frame length and the number of users are finite. A density evolution framework is provided to describe the dynamics of decoding, and fundamental limits are found on the maximum channel load (i.e., the number of active users per time slot) that allows reliable communication (successful decoding). Finally, scaling laws are established, describing the non-asymptotic relation between the probability of error, the number of users, and the channel load.

Age of Information (AoI) is studied in two-user broad-cast networks with feedback, and lower and upper bounds are derived on the expected weighted sum AoI of the users. In particular, a class of simple coding actions is considered and within this class, randomized and deterministic policies are devised. Explicit conditions are found for symmetric dependent channels under which coded randomized policies strictly outperform the corresponding uncoded policies. Similar behaviour is shown numerically for deterministic policies.

International audience

In new applications of data compression, it is desired to have random access to any block of the compressed dataset (without the need to decompress the entire compressed sequence and thus accessing all the stored bits in memory). In this work, we analyze the problem of universal data compression with random access. Building on the work of Mazumdar, Chandar, and Wornell (2015), we discuss a systematic scheme to achieve close to optimal compression with finite random access. We first analyze the performance of the scheme for i.i.d sources. Using the gained intuition, for the more general class of Markov sources, we show the existence of finite random access compression schemes. Finally, we discuss a generic scheme which can be used to convert any universal compressor (e.g., Lempel-Ziv based schemes) into a finite random access universal compressor.

An erasure broadcast network is considered with two disjoint sets of receivers: a set of weak receivers with all-equal erasure probabilities and equal cache sizes and a set of strong receivers with all-equal erasure probabilities and no cache memories. Lower and upper bounds are presented on the capacity-memory tradeoff of this network (the largest rate at which messages can be reliably communicated for given cache sizes). The lower bound is achieved by means of a joint cache-channel coding scheme and significantly improves over traditional schemes based on the separate cache-channel coding. In particular, it is shown that the joint cache-channel coding offers new global caching gains that scale with the number of strong receivers in the network. The upper bound uses bounding techniques from degraded broadcast channels and introduces an averaging argument to capture the fact that the contents of the cache memories are designed before knowing users' demands. The derived upper bound is valid for all stochastically degraded broadcast channels. The lower and upper bounds match for a single weak receiver (and any number of strong receivers) when the cache size does not exceed a certain threshold. Improved bounds are presented for the special case of a single weak and a single strong receiver with two files and the bounds are shown to match over a large range of cache sizes.

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Two scenarios are considered: 1) when the transmitter has causal knowledge of the channel state (i.e., the state is visible) and 2) when the channel state is unknown at the transmitter, but observations of it are available at the transmitter through feedback (i.e., the state is hidden). In both scenarios, matching outer and inner bounds on the rates of communication are derived and the capacity region is determined. It is shown that similar results carry over to channels with memory and delayed feedback and memoryless compound channels with feedback. When the state is visible, the capacity region has a single-letter characterization and is in terms of a linear program. Two optimal coding schemes are devised that use feedback to keep track of the sent/received packets via a network of queues: a probabilistic scheme and a deterministic backpressure-like algorithm. The former bases its decisions solely on the past channel state information and the latter follows a max-weight queue-based policy. The performance of the algorithms is analyzed using the frameworks of rate stability in networks of queues, max-flow min-cut duality in networks, and finite-horizon Lyapunov drift analysis. When the state is hidden, the capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past $L$ acknowledgments and its achievable rate region approaches the capacity region exponentially fast in $L$ . The second algorithm is a backpressure-like algorithm that performs optimally in the long run.

In this paper, we consider a lossy single-user caching problem with correlated sources. We first describe the fundamental interplay between the source correlations, the capacity of the user's cache, the user's reconstruction distortion requirements, and the final delivery-phase (compression) rate. We then illustrate this interplay using a multivariate Gaussian source example and a binary symmetric source example. To fully explore the effect of the user's distortion requirements, we formulate the caching problem using f-separable distortion functions recently introduce by Shkel and Verdú. The class of f-separable distortion functions includes separable distortion functions as a special case, and our analysis covers both the expected- and excess-distortion settings in detail. We also determine what “common information” should be placed in the cache, and what information should be transmitted during the delivery phase. To this end, two new common-information measures are introduced for caching, and their relationship to the common-information measures of Wyner, Gács, and Körner is discussed in detail.

Improved lower bounds are derived on the average and worst case rate-memory tradeoffs of the Maddah-Ali and Niesen-coded caching scenario. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is shown to be less than 2.315 in the worst case scenario and 2.507 in the average-case scenario.

This paper considers a K-user Gaussian broadcast channel (BC) where receivers are equipped with cache memories. Lower and upper bounds are established on the capacity-memory tradeoff, i.e., the largest rate achievable for given cache-memories. The lower bound is based on a joint cache-channel coding scheme which generalizes the recently proposed piggyback coding to Gaussian BCs with unequal cache sizes. This paper also establishes lower and upper bounds on the global capacity-memory tradeoff, i.e., the maximum capacity-memory tradeoff over all possible cache assignments subject to a total cache memory constraint. The bounds match when the total cache memory is sufficiently large. It is shown that significantly larger rates can be achieved by carefully assigning larger cache memories to weaker receivers. In particular, cache allocation allows communication at rates that are (fundamentally) impossible to achieve with equal cache assignment. This shows the merit in carefully designing the cache size allocation in conjunction with channel qualities.

The downlink of symmetric Cloud Radio Access Networks (C-RANs) with multiple relays and a single receiver is studied. Lower and upper bounds are derived on the capacity. The lower bound is achieved by Marton's coding which facilitates dependence among the multiple-access channel inputs. The upper bound uses Ozarow's technique to augment the system with an auxiliary random variable. The bounds are studied over scalar Gaussian C-RANs and are shown to meet and characterize the capacity for interesting regimes of operation.

The degraded K-receiver broadcast channel (BC) is studied when receivers are aided with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate that can be achieved as a function of the receivers' cache sizes. The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. The paper also provides lower and upper bounds on the global capacity-memory tradeoff of degraded BCs, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers cache-assignment subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, with the thresholds depending on the BC statistics. For a small total cache budget M, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows as M/D, where D denotes the total number of files in the system. For a large total cache budget, it is optimal to assign a positive cache memory to every receiver, where weaker receivers are assigned larger cache memories than stronger receivers. When the total cache budget M exceeds a threshold, then the global capacity-memory tradeoff grows as 1/K.M/D.A uniform cache-assignment policy is suboptimal.

A necessary condition is established for the lossy transmission of correlated sources over a memoryless multiple-access channel (MAC). It is used to derive lower bounds on the symmetric distortions that are achievable over Gaussian and binary adder MACs. When specialized to symmetric Gaussian MACs and Gaussian sources, the new lower bound recovers Lapidoth and Tinguely's max-correlation lower bound (2010) when the channel bandwidth is equal to the source bandwidth, and it improves on it when the channel bandwidth is higher. An analogous condition is also derived for the MAC with correlated sources and feedback.

Improved lower bounds on the worst-case and the average-case rate-memory tradeoffs for the Maddah-Ali&Niesen coded-caching scenario are presented. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is less than 2.315 in the worst-case scenario and less than 2.507 in the average-case scenario.

A class of two-relay diamond networks is studied where the broadcast component is modelled by two independent bit-pipes and the multiple-access component is memoryless. A new upper is derived on the capacity which generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). For binary adder MACs, the upper bound establishes the capacity for all ranges of bit-pipe capacities.

We study the capacity of a broadcast packet-erasure network with receiver caching. The receivers in the network are divided into two groups: A group of strong receivers with small packet erasure probabilities, and a group of weak receivers with large packet erasure probabilities. The weak receivers are provided with local cache memories as compensation for their poor channels. Achievable (lower) and converse (upper) bounds for the optimal capacity-memory tradeoff are derived. The lower bounds are proved using new joint cache-channel coding schemes that significantly outperform naive separate cache-channel coding schemes. For the case of two receivers, the capacity-memory tradeoff is completely characterized for a range of useful cache memory sizes.

A class of diamond networks is studied where the broadcast component is orthogonal and modeled by two independent bit-pipes. New upper and lower bounds on the capacity are derived. The proof technique for the upper bound generalizes the bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The lower bound is based on Marton's coding technique and superposition coding. The bounds are evaluated for Gaussian and binary adder multiple access channels (MACs). For Gaussian MACs, both the lower and upper bounds strengthen the Kang-Liu bounds and establish capacity for interesting ranges of bit-pipe capacities. For binary adder MACs, the capacity is established for all the ranges of bit-pipe capacities.

The problem of multicasting two nested messages is studied over a class of networks known as combination networks. A source multicasts two messages, a common and a private message, to several receivers. A subset of the receivers (called the public receivers) only demand the common message, and the rest of the receivers (called the private receivers) demand both the common and the private message. Three encoding schemes are discussed that employ linear superposition coding, and their optimality is proved in special cases. The standard linear superposition scheme is shown to be optimal for networks with two public receivers and any number of private receivers. When the number of public receivers increases, this scheme stops being optimal. Two improvements are discussed: one using pre-encoding at the source, and one using a block Markov encoding scheme. The rate-regions that are achieved by the two schemes are characterized in terms of feasibility problems. Both inner bounds are shown to be the capacity region for networks with three (or fewer) public and any number of private receivers. Although the inner bounds are not comparable in general, it is shown through an example that the region achieved by the block Markov encoding scheme may strictly include the region achieved by the pre-encoding/linear superposition scheme. Optimality results are founded on the general framework of Balister and Bollobás (2007) for sub-modularity of the entropy function. An equivalent graphical representation is introduced and a lemma is proved that might be of independent interest. Motivated by the connections between combination networks and broadcast channels, a new block Markov encoding scheme is proposed for broadcast channels with two nested messages. The rate-region that is obtained includes the previously known rate-regions. It remains open whether this inclusion is strict.

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modelled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of this hidden Markov chain are available at the transmitter through feedback. Matching outer and inner bounds are derived and the capacity region is determined. The capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past L feedback sequences. Its achievable rate-region approaches the capacity region exponentially fast in L. The second algorithm is a backpressure-like algorithm that performs optimally in the long run.

A class of diamond networks is studied where the broadcast component is modelled by two independent bit-pipes. New upper and lower bounds are derived on the capacity which improve previous bounds. The upper bound is in the form of a max-min problem, where the maximization is over a coding distribution and the minimization is over an auxiliary channel. The proof technique generalizes bounding techniques of Ozarow for the Gaussian multiple description problem (1981) and Kang and Liu for the Gaussian diamond network (2011). The bounds are evaluated for a Gaussian multiple access channel (MAC) and the binary adder MAC, and the capacity is found for interesting ranges of the bit-pipe capacities.

In multiterminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi proposed a receiving strategy, which performs a joint unique decoding of messages of interest along with a subset of messages, which are not of interest. It is now well-known that this provides an achievable region, which is, in general, larger than if the receiver treats all messages not of interest as noise. Nair and El Gamal and Chong, Motani, Garg, and El Gamal independently proposed a generalization called indirect or nonunique decoding where the receiver uses the codebook structure of the messages to uniquely decode only its messages of interest. Nonunique decoding has since been used in various scenarios. The main result in this paper is to provide an interpretation and a systematic proof technique for why nonunique decoding, in all known cases where it has been employed, can be replaced by a particularly designed joint unique decoding strategy, without any penalty from a rate region viewpoint.

Encoding schemes for broadcasting two nested message sets are studied. We start with a simple class of deterministic broadcast channels for which (variants of) linear superposition coding are optimal in several cases [1], [2]. Such schemes are sub-optimal in general, and we propose a block Markov encoding scheme which achieves (for some deterministic channels) rates not achievable by the previous schemes in [1], [2]. We adapt this block Markov encoding scheme to general broadcast channels, and show that it achieves a rate-region which includes the previously known rate-regions1.

In mutiterminal communication systems, signals carrying messages meant for different destinations are often observed together at any given destination receiver. Han and Kobayashi (1981) proposed a receiving strategy which performs a joint unique decoding of messages of interest along with a subset of messages which are not of interest. It is now well-known that this provides an achievable region which is, in general, larger than if the receiver treats all messages not of interest as noise. Nair and El Gamal (2009) and Chong, Motani, Garg, and El Gamal (2008) independently proposed a generalization called indirect or non-unique decoding where the receiver uses the codebook structure of the messages to only uniquely decode its messages of interest. Indirect (non-unique) decoding has since been used in various scenarios. The main result in this paper is to provide an interpretation and a systematic proof technique for why indirect decoding, in all known cases where it has been employed, can be replaced by a particularly designed joint unique decoding strategy, without any penalty from a rate region viewpoint1.

In this paper, we study delivery of two nested message sets over combination networks with an arbitrary number of receivers, where a subset of receivers (public receivers) demand only the lower priority message and a subset of receivers (private receivers) demand both the lower and the higher priority messages. We give a complete rate region characterization over combination networks with three public and any number of private receivers, where achievability is through linear coding. Our encoding scheme is general and characterizes an achievable region for arbitrary number of public and private receivers.

We consider communication of two degraded message sets over graphs where a common source sends two prioritized messages (a common and a private message) to several receivers. All receivers require the common message and a subset of the receivers require both the common and private messages. In this paper, we consider the case where all but two of the receivers require both messages. We provide an outer-bound on the rate region that depends on graph properties. We prove that this bound is achievable by using carefully selected linear operations at the network nodes. The achievability proof is built on our result in [14] and is illustrating potential connections of communication over deterministic channels and communication over graphs.

Channel allocation was extensively studied in the framework of cellular networks. But the emergence of new system concepts, such as cognitive radio systems, has brought this topic into the focus of research again. In this paper, we study in detail the problem of competitive multi-radio multi-channel allocation in wireless networks. We study the existence of Nash equilibria in a static game and we conclude that, in spite of the non-cooperative behavior of such devices, their channel allocation results in a load-balancing solution. In addition, we consider the fairness properties of the resulting channel allocations and their resistance to the possible coalitions of a subset of players. Finally, we present three algorithms that achieve a load-balancing Nash equilibrium channel allocation; each of them using a different set of available information.