Communication with Feedback via Posterior Matching

In this paper we describe a general algorithmic scheme for communication over any memoryless channel in the presence of noiseless feedback. The scheme is based on the idea of posterior matching, in which the information still missing at the receiver is extracted from the a-posteriori density function, and matched to any desirable input distribution. We analyze the error probability attained by this scheme for additive noise channels, and show that the well-known Schalkwijk-Kailath scheme for the AWGN channel with average power constraint and the Horstein scheme for the BSC, can be derived as special cases.