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

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2 Author(s)
Ahlswede, R. ; Fak. fur Math., Bielefeld Univ., Germany ; Ning Cai

Whereas the average error capacity region Ra 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 Rm 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 Rm,l for the MAC. For a nice class of deterministic MAC, which we call "seminoisy," we completely characterized Rm,l. For these channels, the Y-input is determined uniquely by the output. Dueck's (1978) example with Ra ≠ Rm and Vanroose's (1988) "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.

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Information Theory, IEEE Transactions on  (Volume:48 ,  Issue: 8 )