Coding schemes for discrete memoryless multicast networks with and without feedback

Coding scheme for discrete memoryless multicast networks with rate-limited feedback from the receivers and relays to the transmitter is proposed. The coding scheme is based on block-Markov coding, joint backward decoding and hybrid relaying strategy. In each block, the relays use partial decode-forward strategy to decode part of the source message. Meanwhile, the receivers and relays use compress-forward strategy to compress their channel outputs and send the compression indices to the transmitter through the feedback links. In the next block, after obtaining the compression indices, the transmitter sends them together with the source message. Each receiver uses backward decoding to jointly decode the source message and all compression indices. It is shown that our coding scheme generalizes Gabbai and Bross's results for the single relay channel with partial feedback, where they proposed coding schemes based on restricted decoding and deterministic partitioning. For the single relay channel with relay-transmitter feedback, our coding scheme can strictly improve on noisy network coding, distributed decode-forward coding and all known lower bounds on the achievable rate in the absence of feedback. Furthermore, motivated by the feedback coding scheme, we propose a new coding scheme for discrete memoryless multicast networks without feedback, which also improves noisy network coding and distributed decode-forward coding.