Achievable Rates and Outer Bound for the Half-Duplex MAC with Generalized Feedback

This paper provides comprehensive coding and outer bound for the half-duplex multiple access channel with generalized feedback (MAC-GF). Two users communicate with one destination over a discrete memoryless channel using time division. Each transmission block is divided into 3 time slots with variable durations: the destination is always in receive mode, while each user alternatively transmits and receives during the first 2 time slots, then both cooperate to send information during the last one. The paper proposes two decode-forward based coding schemes, analyzes their rate regions, and also derives two outer bounds with rate constraints similar to the achievable regions. Both schemes requires no block Makovity, allowing the destination to decode at the end of each block without any delay. In the first scheme, the codewords in the third time slot are superimposed on the codewords of the first two, whereas in the second scheme, these codewords are independent. While the second scheme is simpler, the first scheme helps emphasize the importance of joint decoding over separate decoding among multiple time slots at the destination. For the Gaussian channel, the two schemes with joint decoding are equivalent, as are the two outer bounds. For physically degraded Gaussian channels, the proposed schemes achieve the capacity. Extension to the m-user half-duplex MAC-GF are provided. Numerical results for the Gaussian channel shows significant rate region improvement over the classical MAC and that the outer bound becomes increasingly tight as the inter-user link quality increases.