E.C. van der Meulen

A survey of multi-way channels in information theory: 1961-1976

The advances in the area of multi-way channels during the period 1961-1976 are described. Shannons two-way channel, the multiple-access channel, the interference channel, the broadcast channel, and the relay channel are treated successively. Only channel coding aspects are discussed. Thirty-nine open problems are mentioned.

The discrete memoryless multiple-access channel with cribbing encoders

The capacity regions are determined for various communication situations in which one or both encoders for a multiple access channel crib from the other encoder and learn the channel input(s) (to be) emitted by this encoder. Most of the achievability proofs in this paper hinge upon the new concept of backward decoding. Also, the notion of Shannon strategies seems to be of crucial importance. It is demonstrated that in some situations parts of the total cooperation line are achievable. Moreover, it is proved that if the encoders and the decoder are allowed to be nondeterministic, the capacity regions are not increased.

A proof of Marton's coding theorem for the discrete memoryless broadcast channel (Corresp.)

A simple proof using random partitions and typicality is given for Martons coding theorem for broadcast channels.

Distribution estimation consistent in total variation and in two types of information divergence

The problem of the nonparametric estimation of a probability distribution is considered from three viewpoints: the consistency in total variation, the consistency in information divergence, and consistency in reversed-order information divergence. These types of consistencies are relatively strong criteria of convergence, and a probability distribution cannot be consistently estimated in either type of convergence without any restrictions on the class of probability distributions allowed. Histogram-based estimators of distribution are presented which, under certain conditions, converge in total variation, in information divergence, and in reversed-order information divergence to the unknown probability distribution. Some a priori information about the true probability distribution is assumed in each case. As the concept of consistency in information divergence is stronger than that of convergence in total variation, additional assumptions are imposed in the cases of informational divergences. >

Random coding theorems for the general discrete memoryless broadcast channel

Three different communication situations are considered for the general nondegraded discrete memoryless broadcast channel with two components. In the most general situation, common and separate information is sent to both receivers. In another situation, only separate information is sent, and in a third, one Common and one separate message is sent. For each communication situation a random coding inner bound on the capacity region is derived. An example is presented which Shows that in the most general situation the inner bound strictly dominates the family of rates obtained by time-sharing. The capacity region for the general situation is characterized by a limiting expression. The relationship with the degraded broadcast channel and the connection with other multiway channels, such as the channel with two senders and two receivers, is shown.

Partial feedback for the discrete memoryless multiple access channel (Corresp.)

The region Cover and Leung found for the discrete memoryless multiple access channel with feedback to both encoders is proved achievable also with feedback to only one encoder. The novel ideas of nonrandom partitions and restricted decoding are used to avoid list coding techniques.

About the asymptotic accuracy of Barron density estimates

By extending the information-theoretic arguments of previous papers dealing with the Barron-type density estimates, and their consistency in information divergence and chi-square divergence, the problem of consistency in Csiszars /spl phi/-divergence is motivated for general convex functions /spl phi/. The problem of consistency in /spl phi/-divergence is solved for all /spl phi/ with /spl phi/(0)</spl infin/ and /spl phi/(t)=O(t ln t) when t/spl rarr//spl infin/. The problem of consistency in the expected /spl phi/-divergence is solved for all /spl phi/ with t/spl phi/(1/t)+/spl phi/(t)=O(t/sup 2/) when t/spl rarr//spl infin/. Various stronger versions of these asymptotic restrictions are considered too. Assumptions about the model needed for the consistency are shown to depend on how strong these restrictions are.

There is no universal source code for an infinite source alphabet

Shows that a discrete infinite distribution with finite entropy cannot be estimated consistently in information divergence. As a corollary the authors show that there is no universal source code for an infinite source alphabet over the class of all discrete memoryless sources with finite entropy. >

Reliable transmission of two correlated sources over an asymmetric multiple-access channel (Corresp.)

Necessary and sufficient conditions are derived for the transmission of two arbitrarily correlated sources over a discrete memoryless asymmetric multiple-access channel. It is shown that in this situation the classical separation principle of Shannon (the factorization of the joint source-channel transmission problem into separate source and channel coding problems) applies. This asymmetric case is the first non-trivial situation of a multiple-access channel with arbitrarily correlated sources in which the sufficient conditions found for the reliable transmission of the sources over the channel turn out to be necessary as well. Furthermore, it is demonstrated that these necessary and sufficient conditions continue to hold if feedback is available to one or both of the encoders.

Uniquely decodable codes for deterministic relay channels

The deterministic relay channel is analyzed and explicit code constructions for all binary and all ternary/binary channels are given. An explicit set of equivalence conditions is used to make a classification of all such relay channels, for which also the capacity is evaluated. The coding problem is then reduced to finding all possible output sequences of a certain finite-state channel determined by the relay coding strategy. The channel states correspond to the possible relay memory contents. For some relay channels capacity is reached by using simple uniquely decodable codes, thus establishing the zero-error capacity of those channels with finite-memory relay strategies. For other relay channels the relay memory must be arbitrarily large to achieve zero-error rates arbitrarily close to capacity. One such code construction is given. It is not known whether there exist relay channels for which the zero-error capacity is strictly smaller than the average-error capacity. The code construction problem for the semideterministic relay channel and for the nonsynchronized relay channel is briefly considered. >