On the capacity of the discrete memoryless broadcast channel with feedback

A coding scheme for the discrete memoryless broadcast channel with {noiseless, noisy, generalized} feedback is proposed, and the associated achievable region derived. The scheme is based on a block-Markov strategy combining the Marton scheme and a lossy version of the Gray-Wyner scheme with side information. In each block, the transmitter sends fresh data and update information that allows the receivers to improve the channel outputs observed in the previous block. For a generalization of Dueck's broadcast channel, our scheme achieves the noiseless-feedback capacity, which is strictly larger than the no-feedback capacity. For a generalization of Blackwell's channel and when the feedback is noiseless, our new scheme achieves rate points that are outside the no-feedback capacity region. It follows by a simple continuity argument that for both these channels and when the feedback noise is sufficiently low, our scheme improves on the no-feedback capacity even when the feedback is noisy.