Successive segmentation-based coding for broadcasting over erasure channels

We study a successive segmentation-based coding scheme for broadcasting a binary source over a multi-receiver erasure broadcast channel. Each receiver has a certain demand on the fraction of source symbols to be reconstructed, and its channel is a memoryless erasure channel. We study the minimum achievable latency at the source to simultaneously meet all the receiver constraints. We consider a class of schemes that partition the source sequence into multiple segments and apply a systematic erasure code to each segment. We formulate the optimal choice of segment sizes and code-rates in this class of schemes as a linear programming problem and provide an explicit solution.We further show that the optimal solution can be interpreted as a successive segmentation scheme that naturally adjusts when users are added or deleted from the system. Numerical plots indicate significant gains over a baseline separation-based coding scheme.