Rudolf Ahlswede

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].

The Complete Intersection Theorem for Systems of Finite Sets

We are concerned here with one of the oldest problems in combinatorial extremal theory. It is readily described after we have made a few conventions. ‫ގ‬ denotes the set of

Elimination of correlation in random codes for arbitrarily varying channels

SummaryThe author determines for arbitrarily varying channelsa)the average error capacity andb)the maximal error capacity in case of randomized encoding. A formula for the average error capacity in case of randomized encoding was announced several years ago by Dobrushin ([3]). Under a mild regularity condition this formula turns out to be valid and follows as consequence from either a) or b).

Strong converse for identification via quantum channels

We present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma. The new method is a generalization to quantum communication channels of Ahlswedes (1979, 1992) approach to classical channels. It involves a development of explicit large deviation estimates to the case of random variables taking values in self-adjoint operators on a Hilbert space. This theory is presented separately in an appendix, and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems.

Common randomness in information theory and cryptography. II. CR capacity

For pt.I see ibid., vol.39, p.1121, 1993. The common randomness (CR) capacity of a two-terminal model is defined as the maximum rate of common randomness that the terminals can generate using resources specified by the given model. We determine CR capacity for several models, including those whose statistics depend on unknown parameters. The CR capacity is shown to be achievable robustly, by common randomness of nearly uniform distribution no matter what the unknown parameters are. Our CR capacity results are relevant for the problem of identification capacity, and also yield a new result on the regular (transmission) capacity of arbitrarily varying channels with feedback.

On source coding with side information via a multiple-access channel and related problems in multi-user information theory

A simple proof of the coding theorem for the multiple-access channel (MAC) with arbitrarily correlated sources (DMCS) of Cover-El Carnal-Salehi, which includes the results of Ahlswede for the MAC and of Slepian-Wolf for the DMCS and the MAC as special cases, is first given. A coding theorem is introduced and established for another type of source-channel matching problem, i.e., a system of source coding with side information via a MAC, which can be regarded as an extension of the Ahlswede-Korner-Wyner type noiseless coding system. This result is extended to a more general system with several principal sources and several side information sources subject to cross observation at the encoders in the sense of Han. The regions are shown to be optimal in special situations. Duecks example shows that this is in general not the case for the result of Cover-El Gamal-Salehi and the present work. In another direction, the achievable rate region for the module-two sum source network found by Korner-Marton is improved. Finally, some ideas about a new approach to the source-channel matching problem in multi-user communication theory are presented. The basic concept is that of a correlated channel code. The approach leads to several new coding problems.

Hypothesis testing with communication constraints

A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, H_{0}: P_{XY} against H_{1}: P_{\={XY}} , is considered when the statistician has direct access to Y data but can be informed about X data only at a preseribed finite rate R . For any fixed R the smallest achievable probability of an error of type 2 with the probability of an error of type 1 being at most \epsilon is shown to go to zero with an exponential rate not depending on \epsilon as the sample size goes to infinity. A single-letter formula for the exponent is given when P_{\={XY}} = P_{X} \times P_{Y} (test against independence), and partial results are obtained for general P_{\={XY}} . An application to a search problem of Chernoff is also given.

An Inequality for the Weights of Two Families of Sets, Their Unions and Intersections

then ~(A) fi(B) < 7(A v B) cS(A A B) for all A, B ~ S, (2) where e(A) = ~(a~A) e(a) and A v B = {awb; aeA, b~B} and A A B = {ac~b; a~A, b~B}. Since every distributive lattice can be embedded in the subsets of some set we get an immediate Corollary. If S is a distributive lattice and (2) holds whenever A, B each contain exactly one point of S then (2) always holds. Here S, A, B may be infinite. Our theorem contains as special cases results of Anderson, Daykin, Fortuin, Ginibre, Greene, Holley, Kasteleyn, Kleitman, Seymour, West and others 1. We discovered it whilst guests at the Mathematisches Forschungsinstit ut Oberwolfach and thank all concerned for their kindness to us.

On Perfect Codes and Related Concepts

The concept of diameter perfect codes, which seems to be a natural generalization of perfect codes (codesattaining the sphere–packing bound) is introduced. This was motivated by the “code–anticode” bound of Delsartein distance regular graphs. This bound in conjunction with the recent complete solutions of diametric problems in the Hamming graph ℌq(n) and the Johnson graph J(n,k)gives a sharpening of the sphere–packing bound. Some necessaryconditions for the existence of diameter perfect codes are given.In the Hamming graph all diameter perfect codes over alphabetsof prime power size are characterized. The problem of tilingof the vertex set of J(n,k) with caps (and maximalanticodes) is also examined.

Arbitrarily varying channels with states sequence known to the sender

The capacity of the arbitrarily varying channels with states sequence known to the sender is determined. The result is obtained with the help of an elimination technique and a robustification technique. It demonstrates once more the power of these techniques.