Arbitrarily varying multiple-access channels - Part II: Correlated senders' side information, correlated messages, and ambiguous transmission
We consider an arbitrarily varying multiple-access channel (AVMAC) W in which the two senders X and Y observe, respectively, the components K-m and L-m of a memoryless correlated source (MCS) {(K-m, L-m)}(m=1)(infinity) with generic rv's (K, L). In Part I of this work [16], it has been shown for the AVMAC without the MCS that in order for the achievable rate region for deterministic codes and the average probability of error criterion to be nonempty, it was sufficient if the AVC were X nonsymmetrizable, y nonsymmetrizable, and Xy nonsymmetrizable. (The necessity of these conditions had been shown earlier by Gubner [7].) Let R-R(W) denote the random code achievable rate region of the AVMAC W. In the present paper, the authors, in effect, trade the loss in achievable rates due to symmetrizability off the gains provided by the MCS. Let R(W, (K, L)) represent the achievable rate region of the AVC W with MCS, for deterministic codes and the average probability of error criterion. There are two main results: 1) if I(K Lambda L) > 0, then R(W, (K, L)) has a nonempty interior iff R-R(W) does too and W is xy nonsymmetrizable; 2) if I(K Lambda L)> 0, H(K/L) > 0, H(L/K) > 0, then the MCS can be transmitted over the AVMAC iff R-R(W) has a nonempty interior and W is xy nonsymmetrizable.
senders' side information correlated messages ahlswede's dichotomy ericson's symmetrizability multiple-access avc