Joint Source-Channel Coding with Time-Varying Channel and Side-Information

Transmission of a Gaussian source over a time-varying Gaussian channel is studied in the presence of time-varying correlated side information at the receiver. A block fading model is considered for both the channel and the side information, whose states are assumed to be known only at the receiver. The optimality of separate source and channel coding in terms of average end-to-end distortion is shown when the channel is static while the side information state follows a discrete or a continuous and quasiconcave distribution. When both the channel and side information states are time-varying, separate source and channel coding is suboptimal in general. A partially informed encoder lower bound is studied by providing the channel state information to the encoder. Several achievable transmission schemes are proposed based on uncoded transmission, separate source and channel coding, joint decoding as well as hybrid digital-analog transmission. Uncoded transmission is shown to be optimal for a class of continuous and quasiconcave side information state distributions, while the channel gain may have an arbitrary distribution. To the best of our knowledge, this is the first example in which the uncoded transmission achieves the optimal performance thanks to the time-varying nature of the states, while it is suboptimal in the static version of the same problem. Then, the optimal \emph{distortion exponent}, that quantifies the exponential decay rate of the expected distortion in the high SNR regime, is characterized for Nakagami distributed channel and side information states, and it is shown to be achieved by hybrid digital-analog and joint decoding schemes in certain cases, illustrating the suboptimality of pure digital or analog transmission in general.Comment: Submitted to IEEE Transactions on Information Theor

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

Correlated Sources In Distributed Networks - Data Transmission, Common Information Characterization and Inferencing

Correlation is often present among observations in a distributed system. This thesis deals with various design issues when correlated data are observed at distributed terminals, including: communicating correlated sources over interference channels, characterizing the common information among dependent random variables, and testing the presence of dependence among observations. It is well known that separated source and channel coding is optimal for point-to-point communication. However, this is not the case for multi-terminal communications. In this thesis, we study the problem of communicating correlated sources over interference channels (IC), for both the lossless and the lossy case. For lossless case, a sufficient condition is found using the technique of random source partition and correlation preserving codeword generation. The sufficient condition reduces to the Han-Kobayashi achievable rate region for IC with independent observations. Moreover, the proposed coding scheme is optimal for transmitting a special correlated sources over a class of deterministic interference channels. We then study the general case of lossy transmission of two correlated sources over a two-user discrete memoryless interference channel (DMIC). An achievable distortion region is obtained and Gaussian examples are studied. The second topic is the generalization of Wyner\u27s definition of common information of a pair of random variables to that of N random variables. Coding theorems are obtained to show that the same operational meanings for the common information of two random variables apply to that of N random variables. We establish a monotone property of Wyner\u27s common information which is in contrast to other notions of the common information, specifically Shannon\u27s mutual information and G\u27{a}cs and K {o}rner\u27s common randomness. Later, we extend Wyner\u27s common information to that of continuous random variables and provide an operational meaning using the Gray-Wyner network with lossy source coding. We show that Wyner\u27s common information equals the smallest common message rate when the total rate is arbitrarily close to the rate-distortion function with joint decoding. Finally, we consider the problem of distributed test of statistical independence under communication constraints. Focusing on the Gaussian case because of its tractability, we study in this thesis the characteristics of optimal scalar quantizers for distributed test of independence where the optimality is both in the finite sample regime and in the asymptotic regime