The concept of the smoothing parameter plays a crucial role in both lattice-based and code-based cryptography, primarily due to its effectiveness in achieving nearly uniform distributions through the addition of noise. Recent research by Pathegama and Barg has determined the optimal smoothing bound for random codes under Rényi Divergence for any order $α\in (1, \infty)$ \cite{pathegama2024r}. Considering the inherent complexity of encoding/decoding algorithms in random codes, our research introduces enhanced structural elements into these coding schemes. Specifically, this paper presents a novel derivation of the smoothing bound for random linear codes, maintaining the same order of Rényi Divergence and achieving optimality for any $α\in (1,\infty)$. We extend this framework under KL Divergence by transitioning from random linear codes to random self-dual codes, and subsequently to random quasi-cyclic codes, incorporating progressively more structures. As an application, we derive an average-case to average-case reduction from the Learning Parity with Noise (LPN) problem to the average-case decoding problem. This reduction aligns with the parameter regime in \cite{debris2022worst}, but uniquely employs Rényi divergence and directly considers Bernoulli noise, instead of combining ball noise and Bernoulli noise.

In this work, we investigate the simultaneous goodness of polar codes and polar lattices. The simultaneous goodness of a lattice or a code means that it is optimal for both channel coding and source coding. The existence of such lattices was proven by using random lattice ensembles. Our work provides an explicit construction based on the polarization technique.

Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for scalar and isotropic Gaussian channels. This paper demonstrates that such relations hold for a much larger class of observation models. We introduce the vector channel where the perturbation is non-isotropic Gaussian noise. For such channels, we derive new representations that connect the$f$-divergence between two distributions to the estimation loss induced by mismatch at the decoder. This approach not only unifies but also greatly extends existing results from both the isotropic Gaussian and classical relative entropy frameworks. Building on this generalization, we extend De Bruijn's identity to mismatched non-isotropic Gaussian models and demonstrate that the connections to generative models naturally follow as a consequence application of this new result.

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation-based approaches underpin many state-of-the-art likelihood estimation models, yet they often face slow convergence and limited theoretical understanding. In this paper, we derive a tighter likelihood bound for noise-driven models to improve both the accuracy and efficiency of maximum likelihood learning. Our key insight extends the classical Kullback–Leibler (KL) divergence–Fisher information relationship to arbitrary noise perturbations, going beyond the Gaussian assumption and enabling structured noise distributions. This formulation allows flexible use of randomized noise distributions that naturally account for sensor artifacts, quantization effects, and data distribution smoothing, while remaining compatible with standard diffusion training. Treating the diffusion process as a Gaussian channel, we further express the mismatched entropy between data and model, showing that the proposed objective upper-bounds the negative log-likelihood (NLL). In experiments, our models achieve competitive NLL on CIFAR-10 and state-of-the-art results on ImageNet across multiple resolutions, all without data augmentation, and the framework extends naturally to discrete data.

This work presents an extension of the Construction πAlattices proposed by Huang and Narayanan, to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders, in contrast to natural orders in prior works. Exploiting this map, we analyse the performance of the resulting multilevel lattice codes and highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover, it is shown that there is a sequence of Construction πAlattices that attain with high probability the Poltyrev-limit.

This paper aims to build a bridge between the probabilistic shaping and the geometric shaping for lattice codes from the perspective of polar lattices. We prove that when performing the lattice Gaussian shaping on polar lattices, a shaping lattice As which is good for the so-called discrete additive white Gaussian noise (AWGN) channel is constructed indeed, and the shaping process is equivalent to the modulo As operation within a multi-level decoding manner. To achieve the power-constraint AWGN channel capacity or the rate distortion bound of the i.i.d. Gaussian source, one classical approach is to construct two nested lattices where the fine lattice takes care of the Gaussian noise or the target distortion, and the coarse lattice is responsible for the boundary of the lattice codewords. Another approach is to construct a single lattice and then perform the lattice Gaussian shaping. The former approach falls into the category of geometric shaping, while the latter one is regarded as a type of probabilistic shaping. This work proposes a unified perspective of these two approaches, and provides new evidence on why they are both able to achieve the optimal performance of Gaussian channel coding and source coding problems.

In this work we extend the Construction$\pi_{A}$lattices proposed in [1], to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders in contrast to natural orders in prior works. Exploiting this map, we analyze the performance of the resulting multilevel lattice codes and show via computer simulations their notably reduced computational complexity provided by the multistage decoding.

In this work, we prove that polar lattices, when tailored for lossy compression, are quantization-good in the sense that their normalized second moments approach$\frac{1}{2\pi e}$as the dimension of lattices increases. It has been predicted by Zamir et al. [1] that the Entropy Coded Dithered Quantization (ECDQ) system using quantization-good lattices can achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous work [2], we established that polar lattices are indeed capable of attaining the same objective. It is reasonable to conjecture that polar lattices also demonstrate quantization goodness in the context of lossy compression. This study confirms this hypothesis.

In this paper, a deterministic sampling decoding strategy for multiple-input multiple output (MIMO) systems is studied, which performs probabilistic searching according to a probability threshold in the lattice Gaussian distribution. Motivated by model probabilistic twin (MPT), the randomness in obtaining the target decoding solution is overcome by the proposed probabilistic searching decoding (PSD) algorithm, which brings considerable decoding gains in both performance and complexity. Specifically, the decoding radius of PSD is derived while the decoding complexity in terms of the number of visited nodes during the searching is also upper bounded, leading to an explicit decoding trade-off. Meanwhile, we generalize PSD by the mechanism of candidate protection so that it enjoys a flexible performance between the suboptimal successive interference cancelation (SIC) decoding and the optimal maximum likelihood (ML) decoding by adjusting the initial search size$K$. Methods for further optimization and complexity reduction of the proposed PSD algorithm are also given. Finally, simulation results based on MIMO detection are presented to confirm the tractable and flexible decoding trade-off of the proposed PSD algorithm.

Abstract Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post-quantum public-key cryptography. As the standardization process takes place, optimizing specific parts of proposed schemes, e.g., Bernoulli sampling and integer Gaussian sampling, becomes a worthwhile endeavor. In this work, we propose a novel Bernoulli sampler based on polar codes, dubbed “polar sampler”. The polar sampler is information theoretically optimum in the sense that the number of uniformly random bits it consumes approaches the entropy bound asymptotically. It also features quasi-linear complexity and constant-time implementation. An integer Gaussian sampler is developed using multilevel polar samplers. Our algorithm becomes effective when sufficiently many samples are required at each query to the sampler. Security analysis is given based on Kullback–Leibler divergence and Rényi divergence. Experimental and asymptotic comparisons between our integer Gaussian sampler and state-of-the-art samplers verify its efficiency in terms of entropy consumption, running time and memory cost. We envisage that the proposed Bernoulli sampler can find other applications in cryptography in addition to Gaussian sampling.

We propose a lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves the strong secret key capacity in the case of degraded source models, as well as the optimal secret key / public communication rate trade-off. The key ingredients of our scheme are the use of the modulo lattice operation to extract the channel intrinsic randomness, based on the notion of flatness factor, together with a randomized lattice quantization technique to quantize the continuous source. Compared to previous works, we introduce two new notions of flatness factor based on$L^{1}$distance and KL divergence, respectively, which might be of independent interest. We prove the existence of secrecy-good lattices under$L^{1}$distance and KL divergence, whose$L^{1}$and KL flatness factors vanish for volume-to- noise ratios up to$2\pi e$. This improves upon the volume-to- noise ratio threshold$2\pi $of the$L^{\infty }$flatness factor.

Effective and adaptive interference management is required in next generation wireless communication systems. To address this challenge, Rate-Splitting Multiple Access (RSMA), relying on multi-antenna rate-splitting (RS) at the transmitter and successive interference cancellation (SIC) at the receivers, has been intensively studied in recent years, albeit mostly under the assumption of perfect Channel State Information at the Receiver (CSIR) and ideal capacity-achieving modulation and coding schemes. To assess its practical performance, benefits, and limits under more realistic conditions, this work proposes a novel design for a practical RSMA receiver based on model-based deep learning (MBDL) methods, which aims to unite the simple structure of the conventional SIC receiver and the robustness and model agnosticism of deep learning techniques. The MBDL receiver is evaluated in terms of uncoded Symbol Error Rate (SER), throughput performance through Link-Level Simulations (LLS), and average training overhead. Also, a comparison with the SIC receiver, with perfect and imperfect CSIR, is given. Results reveal that the MBDL receiver outperforms by a significant margin the SIC receiver with imperfect CSIR, due to its ability to generate on demand non-linear symbol detection boundaries in a pure data-driven manner.

Abstract We present an overview of quantum-safe cryptography (QSC) with a focus on post-quantum cryptography (PQC) and information-theoretic security. From a cryptographic point of view, lattice and code-based schemes are among the most promising PQC solutions. Both approaches are based on the hardness of decoding problems of linear codes with different metrics. From an information-theoretic point of view, lattices and linear codes can be constructed to achieve certain secrecy quantities for wiretap channels as is intrinsically classical- and quantum-safe. Historically, coding theory and cryptography are intimately connected since Shannon’s pioneering studies but have somehow diverged later. QSC offers an opportunity to rebuild the synergy of the two areas, hopefully leading to further development beyond the NIST PQC standardization process. In this paper, we provide a survey of lattice and code designs that are believed to be quantum-safe in the area of cryptography or coding theory. The interplay and similarities between the two areas are discussed. We also conclude our understandings and prospects of future research after NIST PQC standardisation.

Abstract The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice-based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often impractical, so Ring LWE was introduced as a form of ‘structured’ LWE, trading off a hard to quantify loss of security for an increase in efficiency by working over a well-chosen ring. Another popular variant, Module LWE, generalizes this exchange by implementing a module structure over a ring. In this work, we introduce a novel variant of LWE over cyclic algebras (CLWE) to replicate the addition of the ring structure taking LWE to Ring LWE by adding cyclic structure to Module LWE. We show that the security reductions expected for an LWE problem hold, namely a reduction from certain structured lattice problems to the hardness of the decision variant of the CLWE problem (under the condition of constant rank d). As a contribution of theoretic interest, we view CLWE as the first variant of Ring LWE which supports non-commutative multiplication operations. This ring structure compares favorably with Module LWE, and naturally allows a larger message space for error correction coding.

This paper investigates low-dimensional quantizers from the perspective of complex lattices. We adopt Eisenstein integers and Gaussian integers to define checkerboard lattices$\mathcal {E}_{m}$and$\mathcal {G}_{m}$. By explicitly linking their lattice bases to various forms of$\mathcal {E}_{m}$and$\mathcal {G}_{m}$cosets, we discover the$\mathcal {E}_{m,2}^{+}$lattices, based on which we report the best known lattice quantizers in dimensions 14, 15, 18, 19, 22 and 23. Fast quantization algorithms of the generalized checkerboard lattices are proposed to enable evaluating the normalized second moment (NSM) through Monte Carlo integration.

We consider the problem of secure distributed matrix computation (SDMC), where auserqueries a function of data matrices generated at distributedsourcenodes. We assume the availability of$N$honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called theupload cost, while guaranteeing that no$T$colluding servers can learn any information about the source matrices, and the user cannot learn any information beyond the computation result. We first focus on secure distributed matrix multiplication (SDMM), considering two matrices, and propose a novel polynomial coding scheme using the properties of finite field discrete Fourier transform, which achieves an upload cost significantly lower than the existing results in the literature. We then generalize the proposed scheme to include straggler mitigation, and to the multiplication of multiple matrices while keeping the input matrices, the intermediate computation results, as well as the final result secure against any$T$colluding servers. We also consider a special case, called computation with own data, where the data matrices used for computation belong to the user. In this case, we drop the security requirement against the user, and show that the proposed scheme achieves the minimal upload cost. We then propose methods for performing other common matrix computations securely on distributed servers, including changing the parameters of secret sharing, matrix transpose, matrix exponentiation, solving a linear system, and matrix inversion, which are then used to show how arbitrary matrix polynomials can be computed securely on distributed servers using the proposed procedure.

Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are considered. However, in communications, complex-valued processing is usually of interest. Besides, by the use of dual-polarized transmission as well as by the combination of two time slots or frequencies, four-dimensional (quaternion-valued) approaches become more and more important. Hence, to account for this fact, well-known lattice algorithms and related concepts are generalized in this work. To this end, a brief review of complex arithmetic, including the sets of Gaussian and Eisenstein integers, and an introduction to quaternion-valued numbers, including the sets of Lipschitz and Hurwitz integers, are given. On that basis, generalized variants of two important algorithms are derived: first, of the polynomial-time LLL algorithm, resulting in a reduced basis of a lattice by performing a special variant of the Euclidean algorithm defined for matrices, and second, of an algorithm to calculate the successive minima—the norms of the shortest independent vectors of a lattice—and its related lattice points. Generalized bounds for the quality of the particular results are established and the asymptotic complexities of the algorithms are assessed. These findings are extensively compared to conventional real-valued processing. It is shown that the generalized approaches outperform their real-valued counterparts in complexity and/or quality aspects. Moreover, the application of the generalized algorithms to MIMO communications is studied, particularly in the field of lattice-reduction-aided and integer-forcing equalization.

We consider a key encapsulation mechanism (KEM) based on Module-LWE where reconciliation is performed on the 8-dimensional lattice$E_{8}$, which admits a fast CVP algorithm. Our scheme generates 256 bits of key and requires 3 or 4 bits of reconciliation per dimension. We show that it can outperform Kyber in terms of the modulus$q$with comparable error probability and similar requirements in terms of bandwidth. We prove that our protocol is IND-CPA secure and improves the security level of Kyber by 7.3%.

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and decoding while Markov chain Monte Carlo (MCMC) methods from statistics offer an effective way to solve it. In this paper, the sliced lattice Gaussian sampling algorithm is proposed to further improve the convergence performance of the Markov chain targeting at lattice Gaussian sampling. We demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Meanwhile, the convergence rate of the underlying Markov chain is also investigated, and we show the proposed sliced sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. On the other hand, the decoding performance based on the proposed sampling algorithm is analyzed, where the optimization with respect to the standard deviation σ > 0 of the target lattice Gaussian distribution is given. After that, a judicious mechanism based on distance judgement and dynamic updating for choosing σ is proposed for a better decoding performance. Finally, simulation results based on multiple-input multiple-output (MIMO) detection are presented to confirm the performance gain by the convergence enhancement and the parameter optimization.

In a majority of research on covert communications, knowledge about channel state information (CSI) of main channel and/or warden channel is assumed to be known or partially known. However, a covert user may not afford to perform channel estimation in practice, and acquiring the warden's CSI is even impossible. In this paper, we investigate covert communications over non-coherent Rayleigh fading channels, in both i.i.d. fast fading and slow fading cases. We observe that the purpose of covert communication in many scenarios is to hide the existence of the sender, not the receiver. Therefore, we allow the receiver to work in full-duplex mode such that it can emit artificial noise (AN) while receiving signals simultaneously. We analyse the achievable covert rates with fixed and varying AN power and show that in both fast and slow fading cases, it is possible to achieve a positive covert rate. For the slow fading case, we further extend the proposed strategy to a multi-user scenario, in which multiple other users share the same spectral resource and cause interference at the warden. Extensive simulations are performed to verify the correctness of our analysis, which provide new insights on the AN design problem in non-coherent channels.

In this work, we propose a new construction of polar lattices to achieve the rate-distortion bound of a memoryless Gaussian source. The structure of the proposed polar lattices allows to integrate entropy coding into the lattice quantizer, which greatly simplifies the compression process. The overall complexity of encoding and decoding is O(N log2N) for any target distortion and fixed rate larger than the rate-distortion bound. Moreover, the nesting structure of polar lattices provides solutions to various multi-terminal coding problems. The Wyner-Ziv coding problem for a Gaussian source can be solved by using a capacity-achieving polar lattice for the Gaussian channel, nested with a rate-distortion bound achieving lattice, while the Gelfand-Pinsker problem can be solved in a reversed manner. The polar lattice quantizer is further extended to extract Wyner's common information of a pair of Gaussian sources or multiple Gaussian sources.

The uplink of a Cloud Radio Access Network (C-RAN) architecture is studied, where decoding in the cloud takes place at distributed decoding processors. To mitigate the impact of straggling decoders in the cloud, the cloud re-encodes the received frames via a linear code before distributing them to the decoding processors, which estimate linear combinations of the codewords. Focusing on Gaussian channels, and assuming the use of lattice codes at the users, we derive the computational rates and frame error probabilities at the cloud. The approach differs from Compute-and-Forward in that the combination of codewords is not caused by the channel but purposefully created in the cloud by encoding the received signals to reduce the decoding delay.

Cache-aided content delivery is studied in a multi-server system with P servers and K users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any p out of P servers. Thanks to the availability of multiple servers, which model small-cell base stations (SBSs), demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to the single-server scenario. A joint storage and proactive caching scheme is proposed, which exploits coded storage across the servers, uncoded cache placement at the users, and coded delivery. The delivery latency is studied for both successive and parallel transmissions from the servers. It is shown that, with successive transmissions the achievable average delivery latency is comparable to the one achieved in the single-server scenario, while the gap between the two depends on p, the available redundancy across the servers, and can be reduced by increasing the storage capacity at the SBSs. The optimality of the proposed scheme with uncoded cache placement and MDS-coded server storage is also proved for successive transmissions.

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.

Coprime arrays are a class of sensor arrays that play a crucial role in various signal processing tasks because of their desirable properties such as sparsity and increased degrees of freedom (DOF) of coarrays. In this contribution, a new class of three-dimensional (3D) arrays is constructed from pure cubic fields. By studying the properties of cubic integers, we convert the problem of finding two coprime 3-by-3 integer matrices to that of two coprime integers in the ring of integers of a cubic field, which significantly reduces the design complexity and expands the design space of these matrices. The proposed construction offers naturally commutative matrices and includes generalized circulant matrices as a special case (under certain restriction of a parameter). The surged DOF is guaranteed by the generalized Chinese Remainder Theorem (CRT) for rings and ideals.

A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The nodes are connected wirelessly, hence all transmissions by helper nodes during a repair round are available to all the nodes being repaired. The scheme is simple and practical because of low subpacketization, low I/O cost and low computational cost. Achievability of the minimum-bandwidth regenerating (MBR) point, as well as an interior point, on the optimal storage-repair bandwidth tradeoff curve is shown. The subspace properties derived in the paper provide insight into the general properties of functional regenerating codes.

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and cryptography. In this paper, the slice sampling from Markov chain Monte Carlo (MCMC) is adopted to lattice Gaussian sampling. Firstly, the slice-based sampling algorithm is proposed to sample from lattice Gaussian distribution. Then, we demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Moveover, the convergence rate of the underlying Markov chain is investigated, and we show the proposed slice sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. Finally, simulation results based on MIMO detection are presented to confirm the performance gain by convergence enhancement.

Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend polarization theories to a more general information measure, namely, the Rényi entropy. Our study shows that under conditional Rényi entropies of different orders, the same synthetic sub-channel may exhibit opposite extremal states. This result reveals more insights into the polarization phenomenon on the micro scale (probability pairs) rather than on the average scale (entropy, mutual information, etc.).

In this paper, we continue our previous work on the reduction of algebraic lattices over imaginary quadratic fields for the special case when the lattice is spanned over a two dimensional basis. In particular, we show that the algebraic variant of Gauss's algorithm returns a basis that corresponds to the successive minima of the lattice in polynomial time if the chosen ring is Euclidean.

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity (1/2) log(1+SNR) of the additive white Gaussiannoise (AWGN) channel. Our construction follows the multilevel approach of Forney et al., where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby, fulfilling the requirement of the multilevel lattice construction. We prove that the polar lattices are AWGN-good. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is O(N log N) for any fixed target error probability.

In this paper, we show that any sequence of infinite lattice constellations which is good for the unconstrained Gaussian channel can be shaped into a capacity-achieving sequence of codes for the power-constrained Gaussian channel under lattice decoding and non-uniform signaling. Unlike previous results in the literature, our scheme holds with no extra condition on the lattices (e.g., quantization-goodness or vanishing flatness factor), thus establishing a direct implication between AWGN-goodness, in the sense of Poltyrev and capacity-achieving codes. Our analysis uses properties of the discrete Gaussian distribution in order to obtain precise bounds on the probability of error and achievable rates. In particular, we obtain a simple characterization of the finite-blocklength behavior of the scheme, showing that it approaches the optimal dispersion coefficient for high signal-to-noise ratio. We further show that for low signal-to-noise ratio, the discrete Gaussian over centered lattice constellations cannot achieve capacity, and thus a shift (or “dither”) is essentially necessary.

Lemma 1in the above-titled paper[1]only holds for a center$\mathbf {c}=\mathbf {0}$. Therefore,Lemma 1and its preceding paragraph should be replaced by:

The compute-and-forward (C&F) protocol in quasi-static channels normally employs lattice codes based on the rational integers ℤ, the Gaussian integers ℤ[i], or the Eisenstein integers ℤ[ω], while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for C&F in block-fading channels without CSIT, which is referred to as ring C&F because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Owing to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional C&F based on the ℤ-lattices. By investigating the effect of the Diophantine approximation by algebraic conjugates, we prove that the degrees of freedom (DoFs) of the optimized computation rate are n/L, where n is the number of blocks and L is the number of users.

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. First, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding (BDD) using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.

Existing polar coding schemes for the two-user interference channel follow the original idea of Han and Kobayashi, in which component messages are encoded independently and then mapped by some deterministic functions (i.e., homogeneous superposition coding). In this paper, we propose a new polar coding scheme for the interference channel based on the heterogeneous superposition coding approach of Chong, Motani, and Garg. We prove that fully joint decoding (the receivers simultaneously decode both senders' common messages and the intended sender's private message) in the Han-Kobayashi strategy can be simplified to two types of partial-joint decoding, which are friendly to polar coding with practical decoding algorithms. The proposed coding scheme requires less auxiliary random variables and no deterministic functions and can be efficiently constructed. Furthermore, we extend this result to interference networks and show that partial-joint decoding is a general method for designing heterogeneous superposition polar coding schemes in interference networks.

Bases in the complex field, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we examine the properties and reduction of such lattices. Focusing on algebraic Lenstra-Lenstra-Lovász (ALLL) reduction, we show that to satisfy Lovás condition requires the ring to be Euclidean. The proposed algorithm can be used to design network coding matrices in compute-and-forward (C & F).

Repair of multiple partially failed cache nodes is studied in a distributed wireless content caching system, where r out of a total of n cache nodes lose part of their cached data. Broadcast repair of failed cache contents at the network edge is studied; that is, the surviving cache nodes transmit broadcast messages to the failed ones, which are then used, together with the surviving data in their local cache memories, to recover the lost content. The trade-off between the storage capacity and the repair bandwidth is derived. It is shown that utilizing the broadcast nature of the wireless medium and the surviving cache contents at partially failed nodes significantly reduces the required repair bandwidth per node.

Cache-aided content delivery is studied in a multi-server system with P servers and K users, each equipped with a local cache memory. In the delivery phase, each user connects randomly to any ρ out of P servers. Thanks to the availability of multiple servers, which model small base stations with limited storage capacity, user demands can be satisfied with reduced storage capacity at each server and reduced delivery rate per server; however, this also leads to reduced multicasting opportunities compared to a single server serving all the users simultaneously. A joint storage and proactive caching scheme is proposed, which exploits coded storage across the servers, uncoded cache placement at the users, and coded delivery. The delivery latency is studied for both successive and simultaneous transmission from the servers. It is shown that, with successive transmission the achievable average delivery latency is comparable to that achieved by a single server, while the gap between the two depends on ρ, the available redundancy across servers, and can be reduced by increasing the storage capacity at the SBSs.

In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple point-to-point polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder.

Explicit coding schemes are proposed to achieve the rate-distortion function of the Heegard-Berger problem using polar codes. Specifically, a nested polar code construction is employed to achieve the rate-distortion function for doubly symmetric binary sources when the side information may be absent. The nested structure contains two optimal polar codes for lossy source coding and channel coding, respectively. Moreover, a similar nested polar lattice construction is employed when the source and the side information are jointly Gaussian. The proposed polar lattice is constructed by nesting a quantization polar lattice and a capacity-achieving polar lattice for the additive white Gaussian noise channel.

We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. These techniques, along with algebraic properties of the proposed lattices, are then used to construct a sub-optimal de-coupled coding scheme that achieves a constant gap to compound capacity by decoding in a lattice that does not dependent on the channel realization. The gap is characterized in terms of algebraic invariants of the code and is shown to be significantly smaller than previous schemes in the literature. We also exhibit alternative algebraic constructions that achieve the capacity of ergodic (SISO) fading channels.

In this paper, an explicit scheme of wiretap coding based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. First, polar lattices are used to construct secrecy-good lattices for the mod-ΛsGaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mod-Λsfront end and extend polar lattices to the genuine GWC. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both O(N log N log (log N)) . The proposed scheme is proven to be semantically secure.

Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and establish a simple design criterion where the normalized product distance/minimum determinant of the lattice and its dual should be maximized simultaneously. Moreover, we propose concrete lattice codes satisfying this design criterion, which are built from algebraic number fields with constant root discriminant in the single-antenna case, and from division algebras centered at such number fields in the multipleantenna case. The proposed lattice codes achieve strong secrecy and semantic security for all rates Rb- Ce- κ, where Cband Ceare Bob and Eve's channel capacities, respectively, and κ is an explicit constant gap. Furthermore, these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models. Finally, we consider a compound wiretap model with a more restricted uncertainty set, and show that rates Rb- C̅e- κ are achievable, where C̅bis a lower bound for Bob's capacity and C̅eis an upper bound for Eve's capacity for all the channels in the set.

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm in Markov chain Monte Carlo methods is adopted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the limitation of Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, establishes a Markov chain via an independent proposal distribution. We show that the Markov chain arising from this independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is analyzed in terms of the theta series, leading to predictable mixing time. A symmetric Metropolis-Klein algorithm is also proposed, which is proven to be geometrically ergodic.

We consider explicit constructions of multi-level lattice codes that universally approach the capacity of the compound block-fading channel. Specifically, building on algebraic partitions of lattices, we show how to construct codes with negligible probability of error for any channel realization and normalized log-density approaching the Poltyrev limit. Capacity analyses and numerical results on the achievable rates for each partition level are provided. The proposed codes have several enjoyable properties such as constructiveness and good decoding complexity, as compared to random one-level codes. Numerical results for finite-dimensional multi-level lattices based on polar codes are exhibited.

Previous approaches to compute-and-forward (C&F) are mostly based on quantizing channel coefficients to integers. In this work, we investigate the C&F strategy over block fading channels using Construction A over rings, so as to allow better quantization for the channels. Advantages in decoding error probabilities and computation rates are demonstrated, and the construction is shown to outperform the C&F strategy over the integers Z.

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the conventional Gibbs sampling algorithm is demonstrated to be geometrically ergodic in tackling with lattice Gaussian sampling, which means its induced Markov chain converges exponentially fast to the stationary distribution. Moreover, as the exponential convergence rate is dominated by the spectral radius of the forward operator of the Markov chain, a comprehensive analysis is given and we show that the convergence performance can be further enhanced by usages of blocked sampling strategy and choices of selection probabilities.

We propose a lattice coding scheme that achieves the capacity of the compound block-fading channel. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is a refined analysis of the probability of error of the lattice Gaussian distribution in the AWGN channel.

In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the egodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log2N).

We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.

Sampling from a lattice Gaussian distribution is emerging as an important problem in coding and cryptography. This paper gives a further analysis of the independent Metropolis-Hastings-Klein (MHK) algorithm we presented at ISIT 2015. We derive the exact spectral gap of the induced Markov chain, which dictates the convergence rate of the independent MHK algorithm. Then, we apply the independent MHK algorithm to lattice decoding and obtained the decoding complexity for solving the CVP as Õ(e∥Bx-c∥2 / mini ∥b̂i∥2). Finally, the tradeoff between decoding radius and complexity is also established.

As a key sampling scheme in Markov chain Monte Carlo (MCMC) methods, Gibbs sampling is widely used in various research fields due to its elegant univariate conditional sampling, especially in tacking with multidimensional sampling systems. In this paper, a Gibbs-based sampler named as symmetric Metropolis-within-Gibbs (SMWG) algorithm is proposed for lattice Gaussian sampling. By adopting a symmetric Metropolis-Hastings (MH) step into the Gibbs update, we show the Markov chain arising from it is geometrically ergodic, which converges exponentially fast to the stationary distribution. Moreover, by optimizing its symmetric proposal distribution, the convergence efficiency can be further enhanced.

In this work we show that algebraic lattices constructed from error-correcting codes achieve the ergodic capacity of the fading channel. The main ingredients for our construction are a generalized version of the Minkowski-Hlawka theorem and shaping techniques based on the lattice Gaussian distribution. The structure of the ring of integers in a number field plays an important role in the proposed construction. In the case of independent and identically distributed fadings, the lattices considered exhibit full diversity and an exponential decay of the probability of error with respect to the blocklength.

In this paper, we design polar codes and polar lattices for independent identically distributed fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage polarization to achieve the ergodic capacity. For the non-binary input case, polar codes are further extended to polar lattices to achieve the ergodic Poltyrev capacity, i.e., the capacity without power limit. When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the ergodic capacity of fading channels. The coding and shaping are both explicit, and the overall complexity of encoding and decoding is O(N log2N).

In the past, two main approaches for the purpose of authentication, including information-theoretic authentication codes and complexity-theoretic message authentication codes (MACs), were almost independently developed.In this paper, we propose a new cryptographic primitive, namely, artificial-noiseaided MACs (ANA-MACs), which can be considered as both computationally secure and information-theoretically secure.For ANA-MACs, we introduce artificial noise to interfere with the complexity-theoretic MACs and quantization is further employed to facilitate packet-based transmission.With a channel coding formulation of key recovery in the MACs, the generation of standard authentication tags can be seen as an encoding process for the ensemble of codes, where the shared key between Alice and Bob is considered as the input and the message is used to specify a code from the ensemble of codes.Then, we show that the introduction of artificial noise in ANA-MACs can be well employed to resist the key recovery attack even if the opponent has an unlimited computing power.Finally, a pragmatic approach for the analysis of ANA-MACs is provided, and we show how to balance the three performance metrics, including the completeness error, the false acceptance probability, and the conditional equivocation about the key.The analysis can be well applied to a class of ANA-MACs, where MACs with Rijndael cipher are employed.

In this paper, we provide a comprehensive survey on designs and analyses of various relay-destination transceiving schemes, such as zero-forcing (ZF), minimum mean squared error (MMSE), and maximum information rate (MIR) criteria, in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems. In the first part of the paper, we suggest a new framework for the transceiver designs utilizing a decomposable property of the error covariance matrix to give a general insight on the system and make the analysis more tractable. Then, in the second part of the paper, we provide an in-depth analysis on their diversity performance. Our analysis embraces two different scenarios, namely, the diversity-multiplexing tradeoff (DMT) and the diversity-rate tradeoff (DRT). First, we derive compact closed-form expressions for the DMT through tight upper and lower bounds. Then, we observe that while our DMT analysis accurately predicts performance of the ZF and MIR schemes, the MMSE-based designs exhibit a complicated rate-dependent behavior and, thus, are very unpredictable via DMT for finite rate cases. Thus, second, we highlight this interesting observation and characterize the diversity of the MMSE schemes at all finite rates. This leads to closed-form expressions for the DRT which reveals relationship between diversity, spectral efficiency, and the number of antennas at each node. The DRT analysis compliments our work on DMT, and thus, the paper provides a complete understanding on the diversity of MIMO AF relaying systems.

Integer coefficient selection is an important decoding step in the implementation of compute-and-forward (C-F) relaying scheme. Choosing the optimal integer coefficients in C-F has been shown to be a shortest vector problem, which is known to be NP-hard in its general form. Exhaustive search of the integer coefficients is only feasible in complexity for small number of users while approximation algorithms, such as Lenstra-Lenstra-Lovász lattice reduction algorithm, only find a vector within an exponential factor of the shortest vector. An optimal deterministic algorithm was proposed for C-F by Sahraei and Gastpar specifically for the real valued channel case. In this paper, we adapt their idea to the complex valued channel and propose an efficient search algorithm to find the optimal integer coefficient vectors over the ring of Gaussian integers and the ring of Eisenstein integers. A second algorithm is then proposed that generalizes our search algorithm to the integer-forcing multiple-input multiple-output (MIMO) C-F receiver. Performance and efficiency of the proposed algorithms are evaluated through simulations and theoretical analysis.

In this paper, we propose a novel Artificial-Noise-Aided PHYsical layer Phase Challenge-Response Authentication Scheme (ANA-PHY-PCRAS) for practical orthogonal frequency division multiplexing (OFDM) transmission. In this new scheme, Tikhonov-distributed artificial noise is introduced to interfere with the phase-modulated key for resisting potential key-recovery attacks. Then, we address various practical issues for ANA-PHY-PCRAS with OFDM transmission, including correlation among subchannels, imperfect carrier, and timing recoveries. Among them, we show that the effect of sampling offset is significant and a search procedure in the frequency domain should be incorporated for verification. With practical OFDM transmission, the number of uncorrelated subchannels is often insufficient. Hence, we employ a time-separated approach for allocating enough subchannels, and a modified ANA-PHY-PCRAS is proposed to alleviate the discontinuity of channel phase at far-separated time slots. Finally, the key equivocation is derived for the worst case scenario. We conclude that the enhanced security of ANA-PHY-PCRAS comes from the uncertainties of both the wireless channel and introduced artificial noise, compared with the traditional challenge-response authentication scheme implemented at the upper layer.

In this paper, we propose a novel channel estimation method for massive multiple-input multiple-output (MIMO) systems operating in time-division duplexing (TDD) mode. By exploiting the fact that the degrees of freedom of the physical channel matrix are smaller than the number of free parameters, the channel estimation is formulated as an atomic norm denoising problem and solved efficiently via the alternating direction method of multipliers (ADMM). Both theoretical analysis and numerical simulations demonstrate that our proposed method outperforms existing ones in terms of the channel estimation performance.

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcomes the restriction on the standard deviation confronted by the Klein algorithm. It is proven that the Markov chain arising from the proposed MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, making it possible to predict the mixing time of the underlying Markov chain.

Polar lattices have been proved to be able to achieve the strong secrecy capacity of the Mod-Λsadditive white Gaussian noise (AWGN) wiretap channel. In this work, we propose an explicit shaping scheme and extend polar lattice coding to the genuine Gaussian wiretap channel. This shaping technique is based on discrete lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. The construction of polar codes for an asymmetric channel can be converted to that for a related symmetrized channel, and it turns out that this symmetrized channel is equivalent to a scaled Λ/Λ' channel in lattice coding in terms of polarization. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously.

Nested lattices Ae⊂ Abhave previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Aeshould be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.

This paper investigates the diversity order of the minimum mean squared error (MMSE) based optimal transceivers in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems. While the diversity-multiplexing tradeoff (DMT) analysis accurately predicts the behavior of the MMSE receiver for the positive multiplexing gain, it turned out that the performance is very unpredictable via DMT for the case of fixed rates, because MMSE strategies exhibit a complicated rate dependent behavior. In this paper, we establish the diversity-rate tradeoff performance of MIMO AF relaying systems with the MMSE transceivers as a closed-form for all fixed rates, thereby providing a complete characterization of the diversity order together with the earlier work on DMT.

To be considered for an IEEE Jack Keil Wolf ISIT Student Paper Award. Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm - Klein's algorithm yields a distribution close to the lattice Gaussian only if the standard deviation is sufficiently large. In this paper, we propose the Markov chain Monte Carlo (MCMC) method for lattice Gaussian sampling when this condition is not satisfied. In particular, we present a sampling algorithm based on Gibbs sampling, which converges to the target lattice Gaussian distribution for any value of the standard deviation. To improve the convergence rate, a more efficient algorithm referred to as Gibbs-Klein sampling is proposed, which samples block by block using Klein's algorithm. We show that Gibbs-Klein sampling yields a distribution close to the target lattice Gaussian, under a less stringent condition than that of the original Klein algorithm.

Polar lattices, which are constructed from polar codes, are provably good for the additive white Gaussian noise (AWGN) channel. In this work, we propose a new polar lattice construction that achieves the secrecy capacity under the strong secrecy criterion over the mod-Λ Gaussian wiretap channel. This construction leads to an AWGN-good lattice and a secrecy-good lattice simultaneously. The design methodology is mainly based on the equivalence in terms of polarization between the Λ/Λ' channel in lattice coding and the equivalent channel derived from the chain rule of mutual information in multilevel coding.

Sampling from certain probability distribution shows better recovery performance than uniform sampling in literature. However, a comprehensive theoretical analysis concerning more realistic signal models is still lacking. In this paper, we consider the sampling of stochastic processes and random fields in the Fourier domain. We propose a new variable-density sampling and linear reconstruction technique, and prove its theoretical recovery guarantee. For high dimensional random fields, uniform sampling requires a number of samples increasing exponentially with the dimension, while the variable density sampling scheme guarantees faithful recovery performance with a polynomial size of random samples.

In this paper, we propose superposition coding based on the lattice Gaussian distribution to achieve strong secrecy over the Gaussian broadcast channel with one confidential message, with a constant gap to the secrecy capacity (only for the confidential message). The proposed superposition lattice code consists of a lattice Gaussian code for the Gaussian noise and a wiretap lattice code with strong secrecy. The flatness factor is used to analyze the error probability, information leakage and achievable rates. By removing the secrecy coding, we can modify our scheme to achieve the capacity of the Gaussian broadcast channel with one common and one private message without the secrecy constraint.

We propose a new coding scheme using only one lattice that achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel with lattice decoding, which is provable for signal-to-noise ratio SNR > e at present. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but otherwise does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which involves a quantization good lattice as well as an AWGN-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error lattice decoding is almost the same as that of Erez and Zamir, for any rate up to the AWGN channel capacity. We introduce the notion of good constellations, which carry almost the same mutual information as that of continuous Gaussian inputs. We also address the implementation of Gaussian shaping for the proposed lattice Gaussian coding scheme.

We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security proof is the flatness factor, which characterizes the convergence of the conditional output distributions corresponding to different messages and leads to an upper bound on the information leakage. We not only introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel secrecy coding scheme based on the discrete Gaussian distribution over a lattice, which achieves the secrecy capacity to within a half nat under mild conditions. No a priori distribution of the message is assumed, and no dither is used in our proposed schemes.

In this paper we study the performance of Barnes-Wall lattices in a symmetric interference channel, under different types of interference. We are inspired by the work of Jafar [1], in which a scheme is proposed for each type of interference, using a base Q expression for the transmitted signals. This is similar to the multilevel structure of Barnes-Wall lattices. With the advantage of their good performance and the extension in bigger dimensions that using lattices implies, we propose to use Barnes-Wall lattices to improve the performance of each user, under lattice alignment in a symmetric interference channel.

We propose a new coding scheme using only one lattice that, under lattice decoding, achieves the 1/2 log(1 + SNR) capacity of the additive white Gaussian noise (AWGN) channel, when the signal-to-noise ratio SNR > 3. The scheme applies a discrete Gaussian distribution over an AWGN-good lattice, but does not require a shaping lattice or dither. Thus, it significantly simplifies the default lattice coding scheme of Erez and Zamir which additionally involves a quantization-good lattice. Using the flatness factor, we show that the error probability of the proposed scheme under minimum mean-square error (MMSE) lattice decoding is almost the same as that of Poltyrev's coding over an infinite lattice, for any rate up to the AWGN channel capacity.

We propose a simple yet complete lattice-based scheme for secret key generation from Gaussian sources in the presence of an eavesdropper, and show that it achieves strong secret key rates up to 1/2 nat from the optimal in the case of “degraded” source models. The novel ingredient of our scheme is a lattice-hashing technique, based on the notions of flatness factor and channel intrinsic randomness. The proposed scheme does not require dithering.

In this paper, we propose the explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel. We follow the multilevel construction of Forney et al. (i.e., Construction D), where the code on each level is a capacity-achieving polar code for that level. The proposed polar lattices are efficiently decodable by using multistage decoding. Performance bounds are derived to measure the gap to the generalized capacity at given error probability. A design example is presented to demonstrate the performance of polar lattices.

Dithered quantization is widely used in signal processing and coding due to its many desirable properties in theory and in practice. In this paper, we show that dither is unnecessary for Gaussian sources when the flatness factor of the quantization lattice is small. This means that the quantization noise behaves much like that in dithered quantization. In particular, it tends to be uniformly distributed over any fundamental region of the lattice and be uncorrelated with the signal; further, for optimum lattice quantizers, it approaches the rate-distortion bound of Gaussian sources with minimum mean-square error (MMSE) estimation.

The Lenstra-Lenstra-Lovász (LLL) algorithm is a popular lattice reduction algorithm in communications. In this paper, variants of the LLL algorithm with either reduced or fixed complexity are proposed and analyzed. Specifically, the use of effective LLL reduction for lattice decoding is presented, where size reduction is only performed for pairs of consecutive basis vectors. Its average complexity (measured by the number of floating-point operations and averaged over i.i.d. standard normal lattice bases) is shown to be O(n3log n), where n is the lattice dimension. This average complexity is an order lower than previously thought. To address the issue of variable complexity of the LLL algorithm, two fixed-complexity approximations are proposed. One is fixed-complexity effective LLL, for which the first vector of the basis is proven to be bounded in length; the other is fixed-complexity LLL with deep insertion, which is shown to be closely related to the well known V-BLAST algorithm. Such fixed-complexity structures are much desirable in hardware implementation since they allow straightforward constant-throughput implementation.

In this paper, a derandomized algorithm for sampling decoding is proposed to achieve near-optimal performance in lattice decoding. By setting a probability threshold to sample candidates, the whole sampling procedure becomes deterministic, which brings considerable performance improvement and complexity reduction over to the randomized sampling. Moreover, the upper bound on the sample size K, which corresponds to near-maximum likelihood (ML) performance, is derived. We also find that the proposed algorithm can be used as an efficient tool to implement soft-output decoding in multiple-input multiple-output (MIMO) systems. An upper bound of the sphere radius R in list sphere decoding (LSD) is derived. Based on it, we demonstrate that the derandomized sampling algorithm is capable of achieving near-maximum a posteriori (MAP) performance. Simulation results show that near-optimum performance can be achieved by a moderate size K in both lattice decoding and soft-output decoding.

The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's embedding technique is a powerful technique for solving the approximate CVP; yet, its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a bounded distance decoding (BDD) viewpoint. We present two complementary analyses of the embedding technique: we establish a reduction from BDD to Hermite SVP (via unique SVP), which can be used along with any Hermite SVP solver (including, among others, the Lenstra, Lenstra and Lovász (LLL) algorithm), and show that, in the special case of LLL, it performs at least as well as Babai's nearest plane algorithm (LLL-aided successive interference cancellation). The former analysis helps us to explain the folklore practical observation that unique SVP is easier than standard approximate SVP. It is proven that when the LLL algorithm is employed, the embedding technique can solve the CVP provided that the noise norm is smaller than a decoding radius λ1/(2γ) , where λ1is the minimum distance of the lattice, and γ ≈O(2n/4). This substantially improves the previously best known correct decoding bound γ ≈O(2n) . Focusing on the applications of BDD to decoding of multiple-input multiple-output systems, we also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff, and propose practical variants of embedding decoding which require no knowledge of the minimum distance of the lattice and/or further improve the error performance.

We consider a wiretap scenario where the main channel and eavesdropper's channel are modulo lattice Gaussian channels. We prove that nested lattice codes can achieve strong secrecy for this model, which gives considerable insights to tackle the genuine Gaussian wiretap channel. The key tool in our proof is an L1convergence result for the conditional output distributions corresponding to different messages, which follows from the properties of the lattice Gaussian measure. No constraint on the a priori distribution of the message is imposed, which means that the proposed scheme is actually semantically secure. We not only show the existence of lattice codes that are good for secrecy, but also propose the flatness factor as a design criterion.

Lattice precoding is an effective strategy for multiantenna broadcast. In this paper, we show that approximate lattice precoding in multiantenna broadcast is a variant of the closest vector problem (CVP) known as η-CVP. The proximity factors of lattice reduction-aided precoding are defined, and their bounds are derived, which measure the worst-case loss in power efficiency compared to sphere precoding. Unlike decoding applications, this analysis does not suffer from the boundary effect of a finite constellation, since the underlying lattice in multiantenna broadcast is indeed infinite.

In this paper we consider the error performance analysis of lattice alignment for the many-to-one interference channel. An upper bound on the error probability for the first receiver when lattice codes are used is derived. More precisely, we consider the case of joint maximum-likelihood (ML) decoding of the desired signal and the sum of interfering signals, derive the union bound for the error probability in terms of the theta series of these lattices, and show that it is related to the flatness factor.

This paper introduces Golay-paired Hadamard matrices for fast compressed sensing of sparse signals in the time or spectral domain. These sampling operators feature low-memory requirement, hardware-friendly implementation and fast computation in reconstruction. We show that they require a nearly optimal number of measurements for faithful reconstruction of a sparse signal in the time or frequency domain. Simulation results demonstrate that the proposed sensing matrices offer a reconstruction performance similar to that of fully random matrices.

The sampling decoding algorithm randomly samples lattice points and selects the closest one from the candidate list. Although it achieves a remarkable performance gain with polynomial complexity, there are two inherent issues due to random sampling, namely, repetition and missing of certain lattice points. To address these issues, a derandomized algorithm of sampling decoding is proposed with further performance improvement and complexity reduction. Given the sample size K, candidates are deterministically sampled if their probabilities P satisfy the threshold PK ≥ 1/2. By varying K, the decoder with low complexity enjoys a flexible performance between successive interference cancelation (SIC) and maximum-likelihood (ML) decoding.

We employ polar codes as the building blocks of Construction D to construct lattices for the additive white Gaussian noise (AWGN) channel. The construction of these component polar codes is based on the idea of Pedarsani et al. for binary-input memoryless symmetric (BMS) channels. Our lattice construction takes the advantage of the performance gain of polar codes over Reed-Muller codes. Simulation results show the lattices constructed from polar codes outperform the benchmark Barnes-Wall lattices, which are constructed from Reed-Muller codes.

Distributed source coding addresses the compression of correlated sources without communication links among them. This paper is concerned with the Wyner-Ziv problem: coding of an information source with side information available only at the decoder in the form of a noisy version of the source. Both the problems of theoretical analysis and code design are addressed in the framework of multi-dimensional nested lattice coding. For theoretical analysis, accurate computation of the rate-distortion function is given under the high-resolution assumption, and a new upper bound using the derivative of the theta series is derived. For practical code design, several low-complexity techniques are proposed. Compared to the existing Slepian-Wolf coded nested quantization for Wyner-Ziv coding based on one or two-dimensional lattices, our proposed multi-dimensional lattice coding can offer better performance at arguably lower complexity, since it does not require the second stage of Slepian-Wolf coding.

Recently, the statistical restricted isometry property (STRIP) has been formulated to analyze the performance of deterministic sampling matrices for compressed sensing. In this paper, a class of deterministic matrices which satisfy STRIP with overwhelming probability are proposed, by taking advantage of concentration inequalities using Stein's method. These matrices, called orthogonal symmetric Toeplitz matrices (OSTM), guarantee successful recovery of all but an exponentially small fraction of K-sparse signals. Such matrices are deterministic, Toeplitz, and easy to generate. We derive the STRIP performance bound by exploiting the specific properties of OSTM, and obtain the near-optimal bound by setting the underlying sign sequence of OSTM as the Golay sequence. Simulation results show that these deterministic sensing matrices can offer reconstruction performance similar to that of random matrices.

In lattice-coded multiple-input multiple-output (MIMO) systems, optimal decoding amounts to solving the closest vector problem (CVP). Embedding is a powerful technique for the approximate CVP, yet its remarkable performance is not well understood. In this paper, we analyze the embedding technique from a bounded distance decoding (BDD) viewpoint. 1/(2γ)-BDD is referred to as a decoder that finds the closest vector when the noise norm is smaller than λ1/(2γ), where λ1is the minimum distance of the lattice. We prove that the Lenstra, Lenstra and Lovász (LLL) algorithm can achieve 1/(2γ)-BDD for γ ≈ O(2n/4). This substantially improves the existing result γ = O(2n) for embedding decoding. We also prove that BDD of the regularized lattice is optimal in terms of the diversity-multiplexing gain tradeoff (DMT).

Secrecy gain has been proposed as a criterion to design wiretap lattice codes. Its analysis relies on the theta series of a lattice, which is closely related to the union bound on the decoding error probability. In this paper, theta series of trellis codes are computed by using a modified transfer function originally for the union bound. We find that the low SNR region of the union bound dominates the secrecy gain. Numerical results show that trellis codes can achieve a similar or higher secrecy gain with less complexity compared to unimodular lattice codes.

Despite its reduced complexity, lattice reduction-aided decoding exhibits a widening gap to maximum-likelihood (ML) performance as the dimension increases. To improve its performance, this paper presents randomized lattice decoding based on Klein's sampling technique, which is a randomized version of Babai's nearest plane algorithm [i.e., successive interference cancelation (SIC)] and samples lattice points from a Gaussian-like distribution over the lattice. To find the closest lattice point, Klein's algorithm is used to sample some lattice points and the closest among those samples is chosen. Lattice reduction increases the probability of finding the closest lattice point, and only needs to be run once during preprocessing. Further, the sampling can operate very efficiently in parallel. The technical contribution of this paper is twofold: we analyze and optimize the decoding radius of sampling decoding resulting in better error performance than Klein's original algorithm, and propose a very efficient implementation of random rounding. Of particular interest is that a fixed gain in the decoding radius compared to Babai's decoding can be achieved at polynomial complexity. The proposed decoder is useful for moderate dimensions where sphere decoding becomes computationally intensive, while lattice reduction-aided decoding starts to suffer considerable loss. Simulation results demonstrate near-ML performance is achieved by a moderate number of samples, even if the dimension is as high as 32.

This paper proposes a generalized sequential slotted amplify and forward (GSSAF) strategy for single-antenna wireless cooperative networks. The diversity and multiplexing tradeoff (DMT) is analyzed. Applications to cooperative multiple relay channels, cooperative broadcast channels (CBC) and cooperative multiple access channels are considered and the DMT upper bound is proven to be achievable for each case. Other than proposing the best known near-optimal strategy for CBC, another important contribution is to show that GSSAF can be used as a unified strategy to achieve DMT optimality in wireless cooperative networks with unit multiplexing gains.

This paper studies the diversity benefit of different interference alignment solutions. While most research about interference alignment was aiming at deriving or realizing the maximum achievable multiplexing gain, the symbol error rate performance, which can be characterized by the diversity gain is of equal importance. Different interference alignment solutions are classified into two categories called diversity interference alignment and zero-forcing interference alignment. Although these two types of solutions are not distinguishable in terms of the multiplexing gain, this paper will show their difference lies in the fact that they have different diversity gains. In this paper, a K-user (M × N) interference channel is used, with each user sending 1 degree of freedom of information by using interference alignment precoding and receiving filters but without space-time codes. The feasibility conditions for diversity interference alignment to be achieved are analyzed and the diversity orders different solutions can provide are compared. The results imply that diversity interference alignment solutions offer both multiplexing and diversity gains simultaneously. It also tells us two important rules about the interference alignment precoding filters design: an optimal design has to take both desired and interference channel matrices into consideration and the separation of interference alignment precoding filters design and space-time codes design may not be optimal in general.

In this paper, we derive user selection criteria based on the error probability for an actually employed detector for multiuser multiple-input multiple-output (MIMO) systems. We propose a low complexity sequential user selection scheme when a lattice reduction (LR) based MIMO detector is used. We also analyze the diversity gain for combinatorial user selection approaches with a given LR-based detector. From simulation results, we can confirm that the proposed sequential user selection approach can provide a comparable performance to the combinatorial ones with much lower complexity.

Sphere decoding achieves maximum-likelihood (ML) performance at the cost of exponential complexity; lattice reduction-aided decoding significantly reduces the decoding complexity, but exhibits a widening gap to ML performance as the dimension increases. To bridge the gap between them, this paper presents randomized lattice decoding based on Klein's randomized algorithm, which is a randomized version of Babai's nearest plane algorithm. The technical contribution of this paper is two-fold: we analyze and optimize the performance of randomized lattice decoding resulting in reduced decoding complexity, and propose a very efficient implementation of random rounding. Simulation results demonstrate near-ML performance achieved by a moderate number of calls, when the dimension is not too large.

Consider a (1 × 1, ½)Ksymmetric wireless interference network where K single-antenna user-pairs want to achieve ½ degrees of freedom each. It has been proved that it is almost surely infeasible to achieve interference alignment without symbol extension. While it was proved relays can not increase the degree of freedom of wireless interference networks, we show this does not preclude the usefulness of using relays to construct practical solutions to approach interference alignment with finite symbol extensions. Feasibility conditions for relay-aided interference alignment are analyzed and an example about how to design the relaying functions to approach interference alignment is given. Simulation results also justify the use of relays as a practical means to do interference alignment with finite symbol extensions.

Using an infinite-series representation of the bivariate Nakagami-m distribution, the cumulative distribution function (cdf) of channel capacity of the decentralized two-relay network (DTRN) is derived. Subsequently, the ϵ-outage channel capacity can be computed. Based on the theoretical results, we define the forbidden zone of correlation, within which the overall channel capacity is drastically reduced by correlated Nakagami fading. Furthermore, the general expression of the outage capacity is also applicable to any other fading statistics. The analysis presented in this paper should provide useful insight on the placement of cooperative relays in the DTRN.

In this paper, we consider the coding of an independent and identically distributed (i.i.d.) Gaussian source with side information available only at the decoder in the form of a noisy version of the source to be encoded. This problem is known as Wyner-Ziv coding in literature. In this paper, we propose concrete implementation by using the strategy of multi-dimensional nested lattice quantization (NLQ). By investigating various lattices in the dimensions considered, we give some analysis on how lattice properties affect performance. We also propose a method on choosing good coarse lattices in multiple dimensions. By introducing scale factors, we examine the relationship between distortion and scale factor for various rates. As dimension increases to eight and twenty-four, we obtain distortion performance close to the Wyner-Ziv limit. Meanwhile, our scheme is simple without causing long delay and large storage, which is suitable for sensor networks.

We propose a near-optimal relaying strategy for cooperative broadcast channels (CBC), CBC-SSAF, based on the class of sequential slotted amplify and forward (SSAF) strategies. Our strategy allows each destination to act in turn as a relay and forward its previously received signal to other destinations. While CBC-SSAF is not a full multiplexing gain strategy, the loss is negligible when the number of destinations is large. Moreover, CBC-SSAF allows each destination to be protected by the maximum number of extra paths in order to achieve the near-optimal diversity gain in the high multiplexing gain regime. A diversity and multiplexing tradeoff (DMT) lower bound for CBC-SSAF is derived which suggests that our proposed relaying strategy approaches the multiple-input multiple-output (MIMO) DMT upper bound and is therefore asymptotically optimal.

The impact of wireless network coding on multiuser diversity gain is investigated. A generic framework to calculate the CDF of the opportunistic channel gain, for different communication scenarios with a single relay, when scheduling or network coding are used, is presented. The CDF and PDF of the lognormal and Rayleigh opportunistic channels for these scenarios are calculated and the average system capacity is derived. Numerical results show that while wireless network coding most of the time can provide significant throughput gain, for low mean received SNR and high channel variations it may result to lower ergodic capacity than simple opportunistic scheduling, especially when transmission overhearing is required. For these cases, we show that although a coding gain is achieved, there may be a larger reduction on the multiuser diversity gain which results to overall lower average system capacity compare to traditional opportunistic scheduling.

A natural relationship between weighted bit-flipping (WBF) decoding and belief-propagation-like (BP-like) decoding is explored. This understanding can help us develop WBF algorithms from BP-like algorithms. For min-sum decoding, one can find that its WBF algorithm is the algorithm proposed by Jiang et al. For BP decoding, we propose a new WBF algorithm and show its performance advantage. The proposed WBF algorithms are parallelized to achieve rapid convergence. Two efficient simulation-based procedures are proposed for the optimization of the associated thresholds.

Lattice reduction-aided decoding enables significant complexity saving and near-optimum performance in digital communications. Its performance can be characterized by the proximity factors that measure the worst-case gap to exact lattice decoding in terms of the signal-to-noise ratio for given error rate. The proximity factors have been derived in literature for both primal and dual basis reduction, and it has been found that in some cases reducing the dual basis can result in asymptotically smaller proximity factors. In this paper, improved upper bounds on the proximity factors for dual-basis reduction are derived, which are uniformly smaller than those for primal basis reduction.

Since the standard union bound for space–time codes may diverge in quasi-static fading channels, the limit-before-average (LBA) technique has been exploited to derive tight performance bounds. However, it suffers from the computational burden arising from a multidimensional integral. In this paper, efficient bounding techniques for space–time codes are developed in the framework of Gallager bounds. Two closed-form upper bounds, the ellipsoidal bound and the spherical bound, are proposed that come close to simulation results within a few tenths of a decibel. In addition, two novel methods of weight enumeration operating on a further reduced state diagram are presented, which, in conjunction with the bounding techniques, give a thorough treatment of performance bounds for space–time codes.

We study the computation of the dual frame for oversampled filter banks (OFBs) by exploiting Greville's formula, which was derived in 1960 to compute the pseudo inverse of a matrix when a new row is appended. In this paper, we first develop the backward Greville formula to handle the case of row deletion. Based on Greville's formula, we then study the dual frame computation of the Laplacian pyramid. Through the backward Greville formula, we investigate OFBs for robust transmission over erasure channels. The necessary and sufficient conditions for OFBs robust to one erasure channel are derived. A post-filtering structure is also presented to implement the dual frame when the transform coefficients in one subband are completely lost.

The use of Lenstra-Lenstra-Lovasz (LLL) lattice reduction significantly improves the performance of zero-forcing (ZF) and successive interference cancellation (SIC) decoders in multi-input multi-output (MIMO) communications. Capitalizing on the observation that the decision region of SIC is determined by the Gram-Schmidt vectors rather than the basis itself, we propose the use of effective LLL reduction in SIC decoding, where size reduction is only performed for pairs of consecutive basis vectors. We establish the theoretic upper bound O(n3log n) on the average complexity of effective LLL reduction for the i.i.d. Gaussian model of MIMO fading channels, which is an order lower than previously thought. Moreover, an effectively LLL-reduced basis can easily be transformed into the standard LLL-reduced basis for the purpose of ZF decoding.

A natural relationship between weighted bit-flipping (WBF) decoding and message-passing decoding is explored. This understanding can help us develop a dual WBF decoding algorithm from one type of message-passing decoding algorithm and vice versa. For min-sum decoding, one can find that its dual WBF algorithm is the algorithm proposed by Jiang et al. For belief-propagation (BP) decoding, we propose a new WBF algorithm and show its performance advantage. For some high-rate low-density parity-check (LDPC) codes of large row weight, it is shown that the WBF algorithm proposed by Liu and Pados performs extraordinarily well. However, its dual message- passing decoding does not work well. Furthermore, we propose a parallel implementation framework for various WBF algorithms. Compared to serial implementations, various WBF algorithms in their parallel form converge significantly faster and often perform better.

Gallager's second bounding technique, also known as the generalized union bound, is employed to derive a new upper bound on the error probability of space-time codes (STCs) with maximum-likelihood (ML) decoding on quasi-static Rayleigh fading channels. The new bound is distinguished by two characteristics: unlike the classical union bound, the new bound is rapidly convergent and is only a few decibels away from simulation results; and compared with Gallager's first bound, it has better computational efficiency and numerical stability. Hence, the new bound is a useful tool for performance analysis and computer search of good STCs. Moreover, the correlation between fading coefficients is easily accommodated by the new bound. The application of the new bound to convolutional coding on block-fading channels is also demonstrated, and an improved version is derived for the bit-error probability of maximum a posteriori probability decoding

Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound.

In this paper, we propose a new upper bound on the error performance of binary linear codes over block-fading channels by employing Gallager's first- and second-bounding techniques. As the proposed bound is numerically intensive in its general form, we consider two special cases, namely, the spherical bound and the DS2-exponential bound, which are found to be tight in nonergodic and near-ergodic block-fading channels, respectively. The tightness of the proposed bounds is demonstrated for turbo codes. Many existing bounds for quasistatic or fully interleaved fading channels can be viewed as special cases of the proposed Gallager bound.

Lattice decoding enables significant complexity reduction in multi-input multi-output (MIMO) communications. Unlike most work on the lattice-reduction-aided decoding technique, this paper is aimed at a comparative study of primal versus dual basis reduction for approximate lattice decoding. We derive the respective proximity factors for the two methods, which measure the performance gap to maximum-likelihood (ML) decoding. It is found that in many cases reducing the dual can result in smaller proximity factors than reducing the primal basis

We derive upper bounds on the decoding error probability of binary block codes over noncoherent block additive white Gaussian noise (AWGN) and fading channels, with applications to turbo codes. By a block AWGN (or fading) channel, we mean that the carrier phase (or fading) is assumed to be constant over each block but independently varying from one block to another. The union bounds are derived for both noncoherent block AWGN and fading channels. For the block fading channel with a small number of fading blocks, we further derive an improved bound by employing Gallager's first bounding technique. The analytical bounds are compared to the simulation results for a coded block-based differential phase shift keying (B-DPSK) system under a practical noncoherent iterative decoding scheme proposed by Chen et al. We show that the proposed Gallager bound is very tight for the block fading channel with a small number of fading blocks, and the practical noncoherent receiver performs well for a wide range of block fading channels

We present improved differential lattice decoding (DLD) for multi-antenna differential modulation by exploiting both basis reduction and sphere decoding. The extra complexity of DLD is shown to be worthwhile in terms of the obtained performance gain over Clarkson et al.'s decoding scheme. With roughly another fold of complexity of basis reduction, DLD augmented by a local search practically attains the maximum-likelihood decoding performance.

From a lattice viewpoint, Clarkson, Sweldens and Zheng significantly reduced the complexity of multiantenna differential decoding. Their approximate decoding algorithm, however, has not unleashed the full potential of lattice decoding. In this paper, we present several improved algorithms, generally referred to as differential lattice decoding (DLD), for multiantenna communication. We first analyze two distinct approximate DLD algorithms, and then develop an algorithm that exactly finds the closest lattice point in the Euclidean space. This exact DLD is subsequently augmented by local search to compensate for the remaining approximation. The small amount of extra complexity of the exact or augmented DLD is rewarded by a clear performance gain. We find that employing basis reduction is very effective to reduce the overall decoding complexity for high lattice dimensions. Moreover, the dimension of the lattice defined in this paper is independent of the number of receive antennas, which results in not only lower complexity, but also better performance for a multiantenna receiver.

We show that linear prediction (LP)-based decision-feedback detection (DFD) for nondiagonal differential space-time modulation (DSTM) may suffer from a severe performance degradation in continuously fading channels. DSTM constellations that incur no degradation in LP-DFD are identified as those with a diagonal generator. To cater to other constellations, we propose a low-complexity DFD scheme by inserting decision-feedback symbols into the metric of multiple-symbol differential detection.

Linear prediction (LP)-based decision-feedback differential detection (DFDD) only works for diagonal differential space-time modulation (DSTM) when fading is changing fast and continuously. For other constellations, it suffers bad performance. We propose DFDD based on multiple-symbol differential detection (MSDD) for DSTM to cope with continuous fading. A key observation is that the correlation matrix of the received signal can be expressed in terms of DSTM matrices corresponding to the sent information symbols. In this way, decision feedback can be inserted into the MSDD metric, yielding a DF-MSDD receiver while maintaining almost the same performance as MSDD.

Existing work on decision feedback detection (DFD) of differential space-time modulation (DTSM) were largely confined to diagonal constellations. In other works considering nondiagonal constellations, the temporal variation of fading in the DTSM supersymbol duration was ignored. In this paper, we take a close look at the DFD receiver structure for nondiagonal DSTM in temporally correlated fading. We identify the constellations of which the error performance is not influenced by ignorance of fading variation. In addition, by analyzing the error performance, we demonstrate that existing DFD, is however, fundamentally mismatched to other constellations in fast fading. A major conclusion is that diagonal design still plays an important role for the efficacy of DFD for nondiagonal constellation in fast fading.

Novel decision-feedback (DF) linear prediction (LP) receivers, which process multiple samples per symbol interval in conjunction with optimal sample combining, are proposed for differential space-time modulation (DSTM) over Rayleigh fast-fading channels. Performance analysis demonstrates that multisampling DF-LP receivers outperform their symbol-rate sampling counterpart in fast fading substantially. In addition, an asymptotically tight upper bound on the pairwise error probability is derived. In view of this bound, the design criterion of DSTM for fast fading is the same as that for block-wise static fading. To avoid the estimation of the second-order statistics of the channel, a polynomial-model-based DF-LP receiver is proposed. It can approach the performance of the optimum DF-LP receiver at high signal-to noise ratios, provided fading is moderate.

The standard Gaussian approximation (SGA) for error analysis of direct-sequence code-division multiple-access (DS-CDMA) systems is very optimistic in many cases. Improved Gaussian approximation (IGA) is a technique that produces accurate error probabilities, but is still computationally intensive. Simplified IGA (SIGA) has complexity similar to that of SGA and, at the same time, provides sufficient accuracy. In this paper, we consider SIGA for DS-CDMA systems employing random sequences in a band-limited scenario. The validity of IGA for band-limited systems is established in a rigorous mathematical sense. Then a key parameter in SIGA is derived via a frequency-domain approach. Applications to a number of typical chip waveforms, including the popular sinc and raised-cosine pulses, are investigated. Performance comparison with IGA-based lower and upper bounds shows that SIGA yields very accurate probability of error.

Approximate maximum-likelihood noncoherent sequence detection (NSD) for differential space-time modulation (DSTM) in time-selective fading channels is proposed. The starting point is the optimum multiple-symbol differential detection for DSTM that is characterized by exponential complexity. By truncating the memory of the incremental metric, a finite-state trellis is obtained so that a Viterbi algorithm can be implemented to perform sequence detection. Compared to existing linear predictive receivers, a distinguished feature of NSD is that it can accommodate nondiagonal constellations in continuous fading. Error analysis demonstrates that significant improvement in performance is achievable over linear prediction receivers. By incorporating the reduced-state sequence detection techniques, performance and complexity tradeoffs can be controlled by the branch memory and trellis size. Numerical results show that most of the performance gain can be achieved by using an L-state trellis, where L is the size of the DSTM constellation.

Space-time codes increase the transmission rate of a communication system in fading channels significantly. The decoding of space-time codes generally depends on perfect channel estimation. Differential space-time modulation (DSTM) can work, in a noncoherent manner, over continuously fading channels. However, it exhibits an irreducible error floor in time-correlated fading channels. The impact of correlated Rayleigh fading on DSTM is investigated, and a decision-feedback linear prediction receiver for DSTM is presented. Computer simulations show that the linear prediction receiver reduces the error floor substantially.

In this paper, the effect of unmatched despreading chip waveforms for locally generated early and late despreading codes in a coherent delay-locked loop (CDLL) for DS/SS systems is investigated. Linear and nonlinear theories are employed to evaluate the performance of the CDLL. Based on linear theory, optimum despreading chip waveforms are pursued in the sense of minimizing root mean square (RMS) tracking error with both time limited (full response) and time unlimited constraints. Nonlinear analysis shows that the use of designed chip waveforms reduces RMS tracking error and increase mean time to lose lock (MTLL). Both rectangular and sinc chip pulse-shaping waveforms are considered as two widely used examples. It is also found that the designed despreading chip waveforms are optimized for any specified early-late spacing.

This letter describes a novel family of frequency hopping sequences generated by chaotic systems. The sequences give a uniform spread over the entire frequency bandwidth. In addition to having good Hamming correlation properties, they possess ideal linear span. The sequences produce almost as good performance as random hopping patterns when used in frequency hopping code-division multiple-access (FH/CDMA) systems. Many numerical examples based on a digital chaos generator are presented.