Nonconvexity of the capacity region of the multiple-access arbitrarily varying channel subject to constraints

Abstract

The multiaccess arbitrarily varying channel (MAVC) subject to state and input constraints models a channel that is subject to jamming or unknown, time-varying uncertainties. The random-code capacity region has been characterized under two different assumptions. Under the assumption that the random encoders are statistically independent, the capacity region is completely characterized. In addition, it is shown by means of a simple erasure channel that this capacity region, /spl Cscr/, is not always convex. To our knowledge, this is the first example of a synchronous multiple-access channel with a nonconvex capacity region. When the random encoders are permitted to be statistically dependent, the capacity region is denoted by /spl Cscr/~. Clearly /spl Cscr//spl sube//spl Cscr/~. It is known that /spl Cscr/~ is always convex. By considering another erasure channel, it is shown that even when /spl Cscr/ is convex, it is possible for /spl Cscr/ to be a proper subset of /spl Cscr/~. In fact, the set-theoretic difference, /spl Cscr/~//spl Cscr/, has a nonempty interior. Hence, permitting the codebooks to be dependent can increase the capacity region. >