Coding for source-broadcasting over erasure channels with feedback

We study a source-broadcasting problem involving an erasure broadcast channel with feedback. The receivers each require a certain fraction of a source sequence, and we are interested in the minimum latency, or transmission time, required to serve them all. We first show that for a two-user broadcast channel, a point-to-point outer bound can always be achieved. For broadcasting to three users, we propose a queue-based hybrid digital-analog coding scheme that achieves optimal performance for the duration of analog transmissions. We propose a method of characterizing the number of analog transmissions that can be sent, which involves solving a linear program, and furthermore give sufficient conditions for which all users can be optimal. In some cases, we find that users can be point-to-point optimal regardless of their distortion constraints. Finally, we propose a channel coding phase for when the analog transmissions are insufficient in meeting user demands and provide simulations that highlight the benefits of feedback.