During recent years there has been strong interest in a certain source coding problem, which some authors call the "problem of multiple descriptions". Old and new wringing techniques enable us to establish a single--letter characterization of the rate--distrotion region in the case of no excess rate for the joint description. 1 The Result Since the origin of the problem of multiple descriptiona and motivations for its study have already been described in an extensive literature [1]--[9], we present our result immediately. It goes considerably beyond those of [17], where the reader also will find a detailed discussion of previously known results. We are given the following. 1) A sequence (X t ) 1 t=1 of independent and identically distributed random variables with values in a finite set X , that is, a discrete memoryless source (DMS). 2) Three finite reconstruction spaces X 0 , X 1 , and X 2 , together with associated per-- letter distortion measures d i : X \Theta X i ! R ...

ly the problem can be stated as follows: Given A ae f1; : : : ; Mg \Theta f1: : : : ; Ng; jAj ffiMN , M = expfR 1 ng, N = expfR 2 ng, does there exist an A = B \Theta C ae A satisfying (4.2)? This is exactly the problem of Zarankiewics [13] for certain values of the parameters (there exists an extensive literature on this problem for jB j; jC j small). In [17] we showed that the question has in general a negative answer and Dueck [5] proved that also the reduction to a maximal error subcode is in general impossible, because average and maximal error capacity regions can be different. Next observe that the existence of subcodes with weaker properties suffices. It is enough that X n and Y n are almost independent. As a possible approach one might try to achieve this by considering a Quasi--Zarankiewics problem in which the condition A = B \Theta C ae A is replaced by jA " B(j)j (1 \Gamma j)jB j; jA " C(j)j (1 \Gamma j)jC j for j 2 C ; i 2 B...

Witsenhausen's hyperbola bound for the multiple description problem without excess rate in case of a binary source is not right for exact joint reproductions. However, this bound is tight for almost--exact joint reproductions (Theorem 1, conjectured by Witsenhausen). The proof is based on an approximative form of the team guessing lemma for sequences of random variables. (This result may be of interest also for team guessing.) The hyperbola bound is also tight for exact joint reproductions and arbitrarily small, but possible, excess rate (Theorem 2). The proof of this result uses our covering lemma. 1 The Problem of Multiple Descriptions During the last years a strong interest has developed in a certain source--coding problem called the "problem of multiple descriptions". Since the origin of this problem and the motivations for its study have already been extensively described (see [1]--[9]), we begin immediately with the formal setup. Let (X t ) 1 t=1 be a sequence of independent a...

A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a two-user discrete memoryless (DM) multiple-access channel (MAC), three lower bounds on the reliability function are derived. The first one (random coding) is identical to the best known lower bound on the reliability function of DM-MAC. It is shown that the random coding bound is the performance of the average code in the constant composition code ensemble. The second bound (Typical random coding) is the typical performance of the constant composition code ensemble. To derive the third bound (expurgated), we eliminate some of the codewords from the codebook with larger rate. This is the first bound of this type that explicitly uses the method of expurgation for MACs. It is shown that the exponent of the typical random coding and the expurgated bounds are greater than or equal to the exponent of the known random coding bounds for all rate pairs. Moreover, an example is given where the exponent of the expurgated bound is strictly larger. All these bounds can be universally obtained for all discrete memoryless MACs with given input and output alphabets. I.

A strong converse for the Gel’fand-Pinsker channel is established in this paper. The method is then extended to a multiuser scenario. A strong converse is established for the multiple-access Gel’fand-Pinsker channel under the maximum error criterion, and the capacity region is determined. 1.

is my pleasure to thank the many people who made this thesis possible. I would like to sincerely thank my research advisors Professor Sandeep Pradhan and Professor Achilleas Anastasopoulos for their continuous support and encouragement, for the opportunity they gave me to conduct independent research, and for their exemplary respect. Even when I became frustrated with research, meetings with them always left me with new ideas and renewed optimism. Their high standards in research, creativity and insistence on high-level understanding of a problem are qualities I hope to emulate in my own career. I would also like to thank my dissertation committee members, Professor David Neuhoff, Professor Erhan Bayraktar, and Professor Jussi Keppo for accepting to be on my dissertation committee. I am grateful to Professor David Neuhoff for his interest in my research and for sharing his deep knowledge. I am indebted to Professor Bayraktar and Professor Keppo for introducing Mathematical Finance to me, which is related to my future career. I feel grateful to Professor Jussi Keppo for accepting to be on my dissertation committee despite the fact that he was going to be out of