The Posterior Matching Feedback Scheme for Joint Source-Channel Coding with Bandwidth Expansion

When transmitting a Gaussian source over an AWGN channel with an input power constraint and a quadratic distortion measure, it is well known that optimal performance can be obtained using an analog joint source-channel scalar scheme which merely scales the input and output signals. In the case of bandwidth expansion, such a joint source-channel analog scheme attaining optimal performance is no longer simple. However, when feedback is available a simple and sequential analog linear procedure based on the Schalkwijk-Kailath scheme for communication, is optimal. Recently, we have introduced a fundamental feedback communication scheme,termed \textit{posterior matching}, which generalizes the Schalkwijk-Kailath scheme to arbitrary memoryless channels and input distributions. In this paper, we show how the posterior matching scheme can be adapted to the joint source-channel coding setting with bandwidth expansion and a general distortion measure, when feedback is available.