Distortion bounds for broadcasting a binary source over binary erasure channels

We study the problem of broadcasting a binary source over a two-receiver erasure broadcast channel with source-channel bandwidth mismatch under a Hamming distortion measure. Given the distortion constraints of both users, we establish a lower bound for the minimum latency required and show that this bound is at least as tight as the one obtained from the source-channel separation theorem. Our derivation involves adapting an outer bound given by Reznic et al. (2006) for the related quadratic Gaussian source broadcast problem. The key step in our outer bound is to replace the entropy power inequality used by Reznic et al. with a suitable inequality for erasure broadcast channels. For the special case in which the user with the better channel requires lossless reconstruction, we present a coding scheme based on a hybrid digital-analog transmission technique and numerically evaluate both inner and outer bounds.