Finite Dimension Wyner-Ziv Lattice Coding for Two-Way Relay Channel

International audienceTwo-way relay channel (TWRC) models a cooperative communication situation performing duplex transmission via a relay station. For this channel, we have shown previously that a lattice-based physical layer network coding strategy achieves, at the limit of arbitrarily large dimension, the same rate as that offered by the random coding-based regular compress-and-forward. In this paper, we investigate a practical coding scheme using finite dimension lattices and offering a reasonable performance-complexity trade-off. The algorithm relies on lattice based quantization for Wyner-Ziv coding. We characterize the rate region allowed by our coding scheme, discuss the design criteria, and illustrate our results with some numerical examples

Slepian-Wolf Coding Over Cooperative Relay Networks

This paper deals with the problem of multicasting a set of discrete memoryless correlated sources (DMCS) over a cooperative relay network. Necessary conditions with cut-set interpretation are presented. A \emph{Joint source-Wyner-Ziv encoding/sliding window decoding} scheme is proposed, in which decoding at each receiver is done with respect to an ordered partition of other nodes. For each ordered partition a set of feasibility constraints is derived. Then, utilizing the sub-modular property of the entropy function and a novel geometrical approach, the results of different ordered partitions are consolidated, which lead to sufficient conditions for our problem. The proposed scheme achieves operational separation between source coding and channel coding. It is shown that sufficient conditions are indeed necessary conditions in two special cooperative networks, namely, Aref network and finite-field deterministic network. Also, in Gaussian cooperative networks, it is shown that reliable transmission of all DMCS whose Slepian-Wolf region intersects the cut-set bound region within a constant number of bits, is feasible. In particular, all results of the paper are specialized to obtain an achievable rate region for cooperative relay networks which includes relay networks and two-way relay networks.Comment: IEEE Transactions on Information Theory, accepte

Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity

Physical-layer network coding for two-way relay channels

Le codage réseau est apparu comme une technique alternative au routage au niveau de la couche réseau permettant d'améliorer le débit et d'optimiser l'utilisation de la capacité du réseau. Récemment, le codage réseau a été appliqué au niveau de la couche physique des réseaux sans-fil pour profiter de la superposition naturelle des signaux effectuée par le lien radio. Le codage réseau peut être vue comme un traitement interne du réseau pour lequel différentes techniques de relayage peuvent être utilisées. Cette thèse étudie un ensemble de traitements ayant des compromis variés en terme de performance et complexité. Nous considérons le canal bidirectionnel à relais, un modèle de canal de communication typique dans les réseaux coopératifs, où deux terminaux s'échangent mutuellement des messages par l'intermédiaire d'un relais. La communication se déroule en deux phases, une phase à accès multiple et une phase de broadcast. Pour ce scénario, nous analysons, dans une première partie, une stratégie de "decode-and-forward". Nous considérons, pour cette étude, des alphabets de taille finie et nous calculons les probabilités moyennes d'erreur de bout-en-bout en se basant sur la métrique d'exposant d'erreur du codage aléatoire. Puis, nous dérivons les régions des débits atteignables par rapport à une probabilité d'erreur maximale tolérable au niveau de chaque nœud. Dans une deuxième partie de la thèse, nous proposons deux schémas de codage réseau pratiques, avec complexité réduite, qui se basent sur la stratégie de relayage "compress-and-forward" (CF). Le premier schéma utilise un codage en réseau de points imbriqués (nested lattices). Le deuxième schéma est une version améliorée qui permet d'atteindre des débits de données supérieurs pour l'utilisateur qui a les meilleures conditions canal. Nous construisons les régions des débits atteignables par les deux schémas proposés tout en optimisant la répartition du temps alloué à chacune des deux phases de transmission. Après l'étude du régime asymptotique, nous analysons le schéma de codage CF avec des réseaux de points de dimension finie. Nous nous concentrons sur le problème de la transmission analogique où la distorsion est optimisée. Enfin, nous étudions l'application d'un schéma de codage, basé sur la stratégie CF avec des réseaux de points imbriqués, pour le canal bidirectionnel à canaux parallèles. Ainsi, nous présentons deux régions de débits atteignables selon la technique de traitement, conjoint ou séparé, des sous-canaux par le relais.Network coding has emerged as an alternative technique to routing that enhances the throughput at the network layer. Recently, network coding has been applied at the physical layer to take advantage of the natural signal superposition that occurs in the radio link. In this context, the physical-layer network coding can be seen as an in-network processing strategy for which multiple forwarding schemes can be proposed. This thesis investigates a set of processing schemes tailored to the network coding at the physical layer with various compromises between performance and complexity. We consider a two-way relay channel, a typical communication system in cooperative networks, where two terminals communicate with each other via a relay node. This communication occurs during two transmission phases, namely a multiple-access phase and a broadcast phase. For TWRC scenario, we first analyze a decode-and-forward strategy with finite size alphabets. We calculate the end-to-end average error probabilities based on random coding error exponents. Then, we derive the achievable rate regions with respect to a maximal probability of error allowed at each terminal. Next, we propose two low-complexity and practical schemes based on compress-and-forward relaying strategy. The first scheme employs nested lattice coding. The second is an improved version which enables higher data rates for the user experiencing the best channel conditions. We present an information-theoretic framework to reconstruct the achievable rate regions of both schemes by considering optimal time division between both transmission phases. After the asymptotic regime analysis, we study single-layer lattice coding scheme with finite dimension lattices. We focus on the analog transmission problem where the distortion is optimized. Finally, we investigate single-layer lattice coding scheme for parallel Gaussian two-way relay channel. We present two achievable rate regions based on whether the relay processes all the sub-channels jointly or separately.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Source Coding in Networks with Covariance Distortion Constraints

We consider a source coding problem with a network scenario in mind, and formulate it as a remote vector Gaussian Wyner-Ziv problem under covariance matrix distortions. We define a notion of minimum for two positive-definite matrices based on which we derive an explicit formula for the rate-distortion function (RDF). We then study the special cases and applications of this result. We show that two well-studied source coding problems, i.e. remote vector Gaussian Wyner-Ziv problems with mean-squared error and mutual information constraints are in fact special cases of our results. Finally, we apply our results to a joint source coding and denoising problem. We consider a network with a centralized topology and a given weighted sum-rate constraint, where the received signals at the center are to be fused to maximize the output SNR while enforcing no linear distortion. We show that one can design the distortion matrices at the nodes in order to maximize the output SNR at the fusion center. We thereby bridge between denoising and source coding within this setup

Secure Multiterminal Source Coding with Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate --average uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bob --secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a non-zero distortion at Bob can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table