Seminoisy deterministic multiple-access channels: coding theorems for list codes and codes with feedback

Whereas the average error capacity region R_a for the multiple-access channel (MAC) W: X × Y → Z has been known for a long time, very little is known about the capacity region R_m for the maximal error concept (as predicted by Ahlswede in 1971). In spite of great efforts during the past three decades even for some special examples of deterministic MAC, for which the maximal error concept coincides with the concept of unique decodability, the progress has been slow. It is known that the permission of list codes can be of great help, even if list sizes are of negligible rates (cf. the arbitrarily varying channel (AVC) and, especially, Shannon\´s (1948) zero-error capacity problem for the one-way channels). Therefore, it is theoretically appealing to look at their regions R_m,l for the MAC. For a nice class of deterministic MAC, which we call "seminoisy," we completely characterized R_m,l. For these channels, the Y-input is determined uniquely by the output. Dueck\´s (1978) example with R_a ≠ R_m and Vanroose\´s (1988) "noiseless binary switching MAC" with R_a = R_m fall into this class. Finally, for this class, the capacity region R_m,f, which concerns complete feedback, equals R_m,l.