On the deterministic-code capacity of the multiple-access arbitrarily varying channel

Abstract

A method that allows one to decide whether or not the capacity region of a multiple-access arbitrarily varying channel (AVC) has a nonempty interior is discussed. Using the method of types and an approach different from J.H. Jahn (ibid. vol.27, no.3, p.212-226, 1981) this problem is partially solved. The notion of symmetrizability for the two-user AVC as an extension of the same notion for the single-user AVC is considered. It is shown that if a multiple-access AVC is symmetrizable, then its capacity region has an empty interior. For the two-user AVC, this means that at least one (and perhaps both) users cannot reliably transmit information across the channel. More importantly, it is shown that if the channel is suitably nonsymmetrizable, then the capacity region has a nonempty interior, and both users can reliably transmit information across the channel. The proofs rely heavily on a complicated decoding rule. Conditions under which simpler multiple-message decoding techniques might suffice are therefore examined. In particular, conditions under which the universal maximal mutual information decoding rule will be effective are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>