In this paper we introduce a fundamental principle for optimal communication
over general memoryless channels in the presence of noiseless feedback, termed
posterior matching. Using this principle, we devise a (simple, sequential)
generic feedback transmission scheme suitable for a large class of memoryless
channels and input distributions, achieving any rate below the corresponding
mutual information. This provides a unified framework for optimal feedback
communication in which the Horstein scheme (BSC) and the Schalkwijk-Kailath
scheme (AWGN channel) are special cases. Thus, as a corollary, we prove that
the Horstein scheme indeed attains the BSC capacity, settling a longstanding
conjecture. We further provide closed form expressions for the error
probability of the scheme over a range of rates, and derive the achievable
rates in a mismatch setting where the scheme is designed according to the wrong
channel model. Several illustrative examples of the posterior matching scheme
for specific channels are given, and the corresponding error probability
expressions are evaluated. The proof techniques employed utilize novel
relations between information rates and contraction properties of iterated
function systems.

本文提出了一种基本原则，即后验匹配，用于通讯过程中的反馈传输方案，在一定条件下，在广泛类别的无记忆信道和输入分布情况下，实现相对应的互信息以下的任何传输速率，该方案提供了一种优化反馈通讯的统一框架，并证明了 Horstein 方案确实实现了 BSC 容量，同时提供了反馈方案的错误概率表达式和可实现的速率范围。