Capacity-Achieving Coding Scheme for the MAC with Degraded Message Sets and Feedback

The multiple access channel (MAC) with degraded message sets and feedback is considered. We show that feedback does not increase the capacity region of this setting, and present a capacity-achieving coding scheme. The coding scheme is inspired by the posterior matching principle for the memoryless channel, but for two transmitters. It is shown that the recursive design of the transmitters and decoder is also maintained in this multi-user setting, leading to a constructive and simple coding scheme. It is interesting to note that the weak transmitter performs its encoding with respect to the decoder's belief as expected, but the strong encoder performs its encoding with respect to the weak encoder's belief and not the decoder's belief. To the best of our knowledge, this is the first matching scheme for a multi-user setting with finite alphabets and feedback.