Expurgated Bounds for the Asymmetric Broadcast Channel

This work contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two different methods of code expurgation will be used, that will provide two competing error exponents. The second is the derivation of expurgated exponents under the generalized stochastic likelihood decoder (GLD). We prove that the GLD exponents are at least as tight as the maximum between the random coding error exponents derived in an earlier work by Averbuch and Merhav (2017) and one of our ML-based expurgated exponents. By that, we actually prove the existence of hierarchical codebooks that achieve the best of the random coding exponent and the expurgated exponent simultaneously for both users

Asymptotics of Fingerprinting and Group Testing: Capacity-Achieving Log-Likelihood Decoders

We study the large-coalition asymptotics of fingerprinting and group testing, and derive explicit decoders that provably achieve capacity for many of the considered models. We do this both for simple decoders (fast but suboptimal) and for joint decoders (slow but optimal), and both for informed and uninformed settings. For fingerprinting, we show that if the pirate strategy is known, the Neyman-Pearson-based log-likelihood decoders provably achieve capacity, regardless of the strategy. The decoder built against the interleaving attack is further shown to be a universal decoder, able to deal with arbitrary attacks and achieving the uninformed capacity. This universal decoder is shown to be closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the empirical mutual information decoder of Moulin. Joint decoders are also proposed, and we conjecture that these also achieve the corresponding joint capacities. For group testing, the simple decoder for the classical model is shown to be more efficient than the one of Chan et al. and it provably achieves the simple group testing capacity. For generalizations of this model such as noisy group testing, the resulting simple decoders also achieve the corresponding simple capacities.Comment: 14 pages, 2 figure

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on Information Theor

Теоретико-информационное представление виртуализации сетевого канала перехвата

The most difficult task of secure telecommunication systems using symmetric encryption, due to the need for preliminary and resource-intensive organization of secret channels for delivering keys to network correspondents, is key management. An alternative is the generating keys methods through open communication channels. In information theory, it is shown that these methods are implemented under the condition that the channel information rate of correspondents exceeds the rate of the intruder interception channel. The search for methods that provide the informational advantage of correspondents is being updated. The goal is to determine the information-theoretical conditions for the formation of a virtual network and an interception channel, for which the best ratio of information speeds for correspondents is provided compared to the ratio of the original network and interception channel. The paper proposes an information transfer model that includes a connectivity model and an information transfer method for asymptotic lengths of code words. The model includes three correspondents and is characterized by the introduction of an ideal broadcast channel in addition to an errored broadcast channel. The model introduces a source of "noisy" information, which is transmitted over the channel with errors, so the transmission of code words using the known method of random coding is carried out over the channel without errors. For asymptotic lengths of code words, all actions of correspondents in processing and transmitting information in the model are reduced to the proposed method of transmitting information. The use of the method by correspondents within the framework of the transmission model makes it possible to simultaneously form for them a new virtual broadcast channel with information rate as in the original channel with errors, and for the intruder a new virtual broadcast interception channel with a rate lower than the information rate of the initial interception channel. The information-theoretic conditions for deterioration of the interception channel are proved in the statement. The practical significance of the results obtained lies in the possibility of using the latter to assess the information efficiency of open network key formation in the proposed information transfer model, as well as in the development of well-known scientific achievements of open key agreement. The proposed transmission model can be useful for researching key management systems and protecting information transmitted over open channels. Further research is related to the information-theoretic assessment of the network key throughput, which is the potential information-theoretic speed of network key formation.Сложнейшей задачей защищенных телекоммуникационных систем, использующих симметричное шифрование, в связи с необходимостью предварительной и ресурсоемкой организации секретных каналов доставки ключей сетевым корреспондентам, является управление ключами. Альтернативой выступают методы формирования ключей по открытым каналам связи. В теории информации показано, что эти методы реализуются при условии превышения информационной скорости канала корреспондентов над скоростью канала перехвата нарушителя. Актуализируется поиск методов, обеспечивающих получение информационного преимущества корреспондентов. Цель заключается в определении теоретико-информационных условий формирования виртуальных сети и канала перехвата, для которых обеспечивается лучшее у корреспондентов отношение информационных скоростей по сравнению с отношением исходных сети и канала перехвата. В работе предлагается модель передачи информации, включающая модель связности и метод передачи информации для асимптотических длин кодовых слов. Модель включает трех корреспондентов и отличается введением идеального широковещательного канала в дополнение к широковещательному каналу с ошибками. В модели введен источник «зашумляющей» информации, которая передается по каналу с ошибками, поэтому передача кодовых слов с использованием известного метода случайного кодирования производится по каналу без ошибок. Для асимптотических длин кодовых слов все действия корреспондентов по обработке и передаче информации в модели сведены в предлагаемый метод передачи информации. Использование метода корреспондентами в рамках модели передачи позволяет одновременно сформировать для них новый виртуальный широковещательный канал с информационной скоростью, как и в первоначальном канале с ошибками, а для нарушителя новый виртуальный широковещательный канал перехвата со скоростью меньшей информационной скорости первоначального канала перехвата. Теоретико-информационные условия ухудшения канала перехвата доказывается в утверждении. Практическая значимость полученных результатов заключается в возможности использования последних для оценки информационной эффективности открытого сетевого формирования ключей в предложенной модели передачи информации, а также в развитии известных научных достижений открытого ключевого согласования. Предлагаемая модель передачи может быть полезной для проведения исследований систем управления ключами и защиты информации, передаваемой по открытым каналам. Дальнейшие исследования связаны с теоретико-информационной оценкой сетевой ключевой пропускной способности, представляющей собой потенциальную теоретико-информационную скорость формирования сетевого ключа

Asymptotic Estimates in Information Theory with Non-Vanishing Error Probabilities

This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error probabilities for various problems are bounded above by a non-vanishing constant and the spotlight is shone on achievable coding rates as functions of the growing blocklengths. This represents the study of asymptotic estimates with non-vanishing error probabilities. In Part I, after reviewing the fundamentals of information theory, we discuss Strassen's seminal result for binary hypothesis testing where the type-I error probability is non-vanishing and the rate of decay of the type-II error probability with growing number of independent observations is characterized. In Part II, we use this basic hypothesis testing result to develop second- and sometimes, even third-order asymptotic expansions for point-to-point communication. Finally in Part III, we consider network information theory problems for which the second-order asymptotics are known. These problems include some classes of channels with random state, the multiple-encoder distributed lossless source coding (Slepian-Wolf) problem and special cases of the Gaussian interference and multiple-access channels. Finally, we discuss avenues for further research.Comment: Further comments welcom

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

Operational interpretation of Rényi information measures via composite hypothesis testing against product and markov distributions

© 1963-2012 IEEE. We revisit the problem of asymmetric binary hypothesis testing against a composite alternative hypothesis. We introduce a general framework to treat such problems when the alternative hypothesis adheres to certain axioms. In this case, we find the threshold rate, the optimal error and strong converse exponents (at large deviations from the threshold), and the second order asymptotics (at small deviations from the threshold). We apply our results to find the operational interpretations of various Rényi information measures. In case the alternative hypothesis is comprised of bipartite product distributions, we find that the optimal error and strong converse exponents are determined by the variations of Rényi mutual information. In case the alternative hypothesis consists of tripartite distributions satisfying the Markov property, we find that the optimal exponents are determined by the variations of Rényi conditional mutual information. In either case, the relevant notion of Rényi mutual information depends on the precise choice of the alternative hypothesis. As such, this paper also strengthens the view that different definitions of Rényi mutual information, conditional entropy, and conditional mutual information are adequate depending on the context in which the measures are used