Coding schemes for discrete memoryless multicast networks with rate-limited feedback

We propose two coding schemes for discrete memoryless multicast networks with rate-limited feedback from receivers and relays to the transmitter. The coding schemes are based on block Markov coding, joint backward decoding and hybrid relaying strategy. In each block, the receivers and relays compress their outputs and send the compression indices to the transmitter through the feedback links. In the next block, after obtaining 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 schemes strictly improve on noisy network coding and generalize Gabbai and Bross´s results for the single relay channel with partial feedback, where they proposed schemes based on restricted decoding and deterministic partitioning. Motivated by our feedback schemes, we propose a new coding scheme for discrete memoryless multicast networks without feedback.