Capacity Bounds for a Class of Interference Relay Channels

The capacity of a class of Interference Relay Channels (IRC) -the Injective Semideterministic IRC where the relay can only observe one of the sources- is investigated. We first derive a novel outer bound and two inner bounds which are based on a careful use of each of the available cooperative strategies together with the adequate interference decoding technique. The outer bound extends Telatar and Tse's work while the inner bounds contain several known results in the literature as special cases. Our main result is the characterization of the capacity region of the Gaussian class of IRCs studied within a fixed number of bits per dimension -constant gap. The proof relies on the use of the different cooperative strategies in specific SNR regimes due to the complexity of the schemes. As a matter of fact, this issue reveals the complex nature of the Gaussian IRC where the combination of a single coding scheme for the Gaussian relay and interference channel may not lead to a good coding scheme for this problem, even when the focus is only on capacity to within a constant gap over all possible fading statistics.Comment: 23 pages, 6 figures. Submitted to IEEE Transactions on Information Theory (revised version

A Quantum Multiparty Packing Lemma and the Relay Channel

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo's bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be "packed" into a given quantum system. In this article, we use Sen's recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing classical formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.Comment: 20 page

Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the \emph{simultaneous relay channel} (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and \emph{Compress-and-Forward} (CF) must be capable of transmitting information simultaneously to all destinations in such set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users --referred to as DF-DF region--, cooperation is based on CF strategy for both users --referred to as CF-CF region--, and cooperation is based on DF strategy for one destination and CF for the other --referred to as DF-CF region--. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.Comment: 32 pages, 7 figures, To appear in IEEE Trans. on Information Theor

Communication Sécurisée et Coopération dans les Réseaux sans Fil avec Interférences and of their Inverter

In this thesis, we conduct an information-theoretic study on two important aspects of wireless communications: the improvement of data throughput in interference-limited networks by means of cooperation between users and the strengthening of the security of transmissions with the help of feedback.In the first part of the thesis, we focus on the simplest model that encompasses interference and cooperation, the Interference Relay Channel (IRC). Our goal is to characterize within a fixed number of bits the capacity region of the Gaussian IRC, independent of any channel conditions. To do so, we derive a novel outer bound and two inner bounds. Specifically, the outer bound is obtained thanks to a nontrivial extension we propose of the injective semideterministic class of channels, originally derived by Telatar and Tse for the Interference Channel (IC).In the second part of the thesis, we investigate the Wiretap Channel with Generalized Feedback (WCGF) and our goal is to provide a general transmission strategy that encompasses the existing results for different feedback models found in the literature. To this end, we propose two different inner bounds on the capacity of the memoryless WCGF. We first derive an inner bound that is based on the use of joint source-channel coding, which introduces time dependencies between the feedback outputs and the channel inputs through different time blocks. We then introduce a second inner bound where the feedback link is used to generate a key that encrypts the message partially or completely.Dans cette thèse, nous menons une étude dans le cadre de la théorie de l'information sur deux questions importantes de la communication sans fil : l'amélioration du débit de données dans les réseaux avec interférence grâce à la coopération entre utilisateurs et le renforcement de la sécurité des transmissions à l'aide d'un signal de rétroaction.Dans la première partie de la thèse, nous nous concentrons sur le modèle le plus simple qui intègre à la fois l'interférence et la coopération, le canal à relais et interférence ou IRC (Interference Relay Channel). Notre objectif est de caractériser dans un nombre fixe de bits la région de capacité du IRC gaussien. À cette fin, nous dérivons une nouvelle limite supérieure de la capacité et deux stratégies de transmission. La limite supérieure est notamment obtenue grâce à une extension non triviale que nous proposons, de la classe de canaux semi-déterministe et injective à l'origine dérivée par Telatar et Tse pour le canal à interférence.Dans la seconde partie, nous étudions le canal avec espion et rétroaction généralisée ou WCGF (Wiretap Channel with Generalized Feedback). Notre objectif est de développer une stratégie de transmission générale qui englobe les résultats existants pour les différents modèles de rétroaction trouvés dans la littérature. À cette fin, nous proposons deux stratégies de transmission différentes sur la capacité du WCGF sans mémoire. Nous dérivons d'abord une stratégie qui est basée sur le codage source-canal conjoint. Nous introduisons ensuite une seconde stratégie où le signal de rétroaction est utilisé pour générer une clé secrète qui permet de chiffrer le message partiellement ou totalement

A joint time-invariant filtering approach to the linear Gaussian relay problem

In this paper, the linear Gaussian relay problem is considered. Under the linear time-invariant (LTI) model the problem is formulated in the frequency domain based on the Toeplitz distribution theorem. Under the further assumption of realizable input spectra, the LTI Gaussian relay problem is converted to a joint design problem of source and relay filters under two power constraints, one at the source and the other at the relay, and a practical solution to this problem is proposed based on the projected subgradient method. Numerical results show that the proposed method yields a noticeable gain over the instantaneous amplify-and-forward (AF) scheme in inter-symbol interference (ISI) channels. Also, the optimality of the AF scheme within the class of one-tap relay filters is established in flat-fading channels.Comment: 30 pages, 10 figure