In this correspondence, we point out the incorrectness of an upper bound in van der Meulen (Advances in Applied Probability, vol. 3, no. 1, pp. 120-154, 1971) and report the correct relay capacity for one of the examples given there. We also show that, when viewed as a relay-without-delay channel, the capacity of this channel is strictly larger than its classical relay capacity.

Pippenger (1981) showed in a probabilistic way that the capacity of a collision channel with multiplicity feedback is one. In this correspondence, using an Erdos-Renyi type search strategy, we settle a long-standing open problem by giving a constructive proof of this result. Moreover, we prove that two different capacity definitions are equivalent, thereby solving a problem posed by Tsybakov (1985).

Various constructions of authentication codes using spaces related to the general linear group have been proposed and analyzed. In the paper the authors describe two new constructions of Cartesian authentication codes using symplectic spaces. This illustrates the feasibility of codes from spaces based on geometries of the other classical groups.>

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.>

The noiseless coding problem is considered for a discrete memoryless multiple-access channel that is a counterpart to the well-known binary adder channel. Upper and lower bounds on the number of code words in a uniquely decodable code pair are given, from which the zero-error capacity region of the channel is derived. This region coincides with the classical capacity region of this channel. The proof uses the notion of second-order distance of a code. For several values of n and k, good code pairs of block length n are constructed, with the first code being (n,k)-linear. Some of these are found to be optimal. Some convolutional codes are investigated that yield additional good rate pairs.>