János Körner

Information Theory: Coding Theorems for Discrete Memoryless Systems

Csiszr and Krners book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful solving hints, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics.

Broadcast channels with confidential messages

Given two discrete memoryless channels (DMCs) with a common input, it is desired to transmit private messages to receiver 1 rate R_{1} and common messages to both receivers at rate R_{o} , while keeping receiver 2 as ignorant of the private messages as possible. Measuring ignorance by equivocation, a single-letter characterization is given of the achievable triples (R_{1},R_{e},R_{o}) where R_{e} is the equivocation rate. Based on this channel coding result, the related source-channel matching problem is also settled. These results generalize those of Wyner on the wiretap channel and of Korner-Marton on the broadcast Channel.

Source coding with side information and a converse for degraded broadcast channels

Let \{(X_i, Y_i,)\}_{i=1}^{\infty} be a memoryless correlated source with finite alphabets, and let us imagine that one person, encoder 1, observes only X^n = X_1,\cdots,X_n and another person, encoder 2, observes only Y^n = Y_1,\cdots,Y_n . The encoders can produce encoding functions f_n(X^n) and g_n(Y^n) respectively, which are made available to the decoder. We determine the rate region in case the decoder is interested only in knowing Y^n = Y_1,\cdots,Y_n (with small error probability). In Section H of the paper we give a characterization of the capacity region for degraded broadcast channels (DBCs), which was conjectured by Bergmans [11] and is somewhat sharper than the one obtained by Gallager [12].

How to encode the modulo-two sum of binary sources (Corresp.)

How much separate information about two random binary sequences is needed in order to tell with small probability of error in which positions the two sequences differ? If the sequences are the outputs of two correlated memoryless binary sources, then in some cases the rate of this information may be substantially less than the joint entropy of the two sources. This result is implied by the solution of the source coding problem with two separately encoded side information sources for a special class of source distributions.

General broadcast channels with degraded message sets

A broadcast channel with one sender and two receivers is considered. Three independent messages are to be transmitted over this channel: one common message which is meant for both receivers, and one private message for each of them. The coding theorem and strong converse for this communication situation is proved for the case when one of the private messages has rate zero.

Zero-error information theory

The problem of error-free transmission capacity of a noisy channel was posed by Shannon in 1956 and remains unsolved, Nevertheless, partial results for this and similar channel and source coding problems have had a considerable impact on information theory, computer science, and mathematics. We review the techniques, results, information measures, and challenges encountered in this ongoing quest.

Towards a general theory of source networks

A unified approach to multiterminal source coding problems not involving rate-distortion theory is presented. It is shown that, for determining file achievable rate region, attention may be restricted to source networks of a relatively simple structure. A product space characterizafion of the achievable rate region pinpoints the mathematical problem to be solved for getting a single letter characterization. The complexity of this problem depends on a structural condition, viz., the number of encoders of a certain kind in the source network. This approach yields all the known single-letter characterizations of achievable rate regions and a number of new ones for more complex networks. As a digression, for a class of source networks including that of Slepian and Wolf, exponential error bounds are derived which are attainable by universal codes. These bounds are tight in a neighborhood of the boundary of the achievable rate region.

Graph decomposition: A new key to coding theorems

A new and simple method is proposed for finding good encoders both for channels and for sources with side information. This method relies on the continuous version of a graph decomposition result of Lovasz. The presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound. The previous bounds for universal codes of the authors and Marton are also improved.

Sperner capacities

We determine the asymptotics of the largest family of qualitatively 2-independentk-partitions of ann-set, for everyk>2. We generalize a Sperner-type theorem for 2-partite sets of Körner and Simonyi to thek-partite case. Both results have the feature that the corresponding trivial information-theoretic upper bound is tight. The results follow from a more general Sperner capacity theorem for a family of graphs in the sense of our previous work on Sperner theorems on directed graphs.

Entropy splitting for antiblocking corners and perfect graphs

We characterize pairs of convex setsA, B in thek-dimensional space with the property that every probability distribution (p1,...,pk) has a repsesentationpi=al.bi, a∃A, b∃B.Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect graphs.