Katalin Marton

A coding theorem for the discrete memoryless broadcast channel

A coding theorem for the discrete memoryless broadcast channel is proved for the case where no common message is to he transmitted. The theorem is a generalization of the results of Cover and van der Meulen on this problem. The result is tight for broadcast channels having one deterministic component

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.

Error exponent for source coding with a fidelity criterion

For discrete memoryless sources with a single-letter fidelity criterion, we study the probability of the event that the distortion exceeds a level d , if for large block length the best code of given rate R > R(d) is used. Lower and upper exponential bounds are obtained, giving the asymptotically exact exponent, except possibly for a countable set of R values.

A simple proof of the blowing-up lemma (Corresp.)

The blowing-up lemma says that if the probability with respect to a product measure of a set A\subseteq {\cal X}^{n} ({\cal X} finite, n large) is not exponentially small, then its l_{n} -neighborhood has probability almost one for some l_{n} = O(n) . Here an information-theoretic proof of the blowing-up lemma, generalizing it to continuous alphabets, is given.

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.

New bounds for perfect hashing via information theory

Abstract A set of sequences of length t from a b-element alphabet is called k-separated if for every k-tuple of the sequences there exists a coordinate in which they all differ. The problem of finding, for fixed t, b, and k, the largest size N(t, b, k) of a k-separated set of sequences is equivalent to finding the minimum size of a (b, k)-family of perfect hash functions for a set of a given size. We shall improve the bounds for N(t, b, k) obtained by Fredman and Komlos [1]. Korner [2] has shown that the proof in [1] can be reduced to an application of the sub-additivity of graph entropy [3]. He also pointed out that this sub-additivity yields a method to prove non-existence bounds for graph covering problems. Our new non-existence bound is based on an extension of graph entropy to hypergraphs.

Images of a set via two channels and their role in multi-user communication

A technique is presented to determine the region of achievable rates for some source and channel networks. This technique is applied to the solution of a source:network problem that seems to be the simplest illustration of a new typical difficulty in coding for source networks: namely, when the same encoding of a source is required to meet the conflicting demands of 1) supplying side-information to the decoder of another source, and 2) providing direct-information to its own decoder in company with other side-information.

The positive-divergence and blowing-up properties

A property of ergodic finite-alphabet processes, called the blowing-up property, is shown to imply exponential rates of convergence for frequencies and entropy, which in turn imply a positive-divergence property. Furthermore, processes with the blowing-up property-divergence property. Furthermore, processes with the blowing-up property are finitely determined and the finitely determined property plus exponential rates of convergence for frequencies and for entropy implies blowing-up. It is also shown that finitary codings of i.i.d. processes have the blowing-up property.

Measure concentration for Euclidean distance in the case of dependent random variables

Let qn be a continuous density function in n-dimensional Euclidean space. We think of qn as the density function of some random sequence Xn with values in