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.