Feedback Communication Over the BSC with Sparse Feedback times and Causal Encoding

Abstract

Posterior matching uses variable-length encoding of the message controlled by noiseless feedback of the received symbols to achieve high rates for short average blocklengths. Traditionally, the feedback of a received symbol occurs before the next symbol is transmitted. The transmitter optimizes the next symbol transmission with full knowledge of every past received symbol. To move posterior matching closer to practical communication, this paper seeks to constrain how often feedback can be sent back to the transmitter. We focus on reducing the frequency of the feedback while still maintaining the high rates that posterior matching achieves with feedback after every symbol. As it turns out, the frequency of the feedback can be reduced significantly with no noticeable reduction in rate.