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

Whereas the average error capacity region Ra for the MAC W : X ×Y → Z is known for a long time (Ahlswede 71), very little is known about the capacity region Rm for the maximal error concept (as predicted also by Ahlswede in 71). Inspite 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 (c.f. AVC and especially Shannon’s zero–error capacity problem for the one–way channels). Therefore it is theoretically appealing to look at their regions Rm,l for the MAC. For a nice class of deterministic MAC, which we call “semi–noisy”, we completely characterized Rm,l. For these channels the Y–input is determined uniquely by the output. Dueck’s example with Ra 6= Rm and Vanroose’s “Noiseless binary switching MAC” with Ra = Rm fall into this class. Finally, for this class the capacity region Rm,f , which concerns complete feedback, equals Rm,l.