Optimal Feedback Communication Via Posterior Matching
Optimal Feedback Communication Via Posterior Matching
复制标题
通过后验匹配的最佳反馈通信
DOI：
10.1109/tit.2011.2104992
复制
发表时间：
2009
影响因子：
2.5
通讯作者：
M. Feder
中科院分区：
文献类型：
--
作者：
O. Shayevitz;M. Feder
在本文中，我们介绍了一个基本原则，在一般的无记忆信道中存在的无噪声反馈，称为后匹配的最佳通信。使用这一原则，我们设计了一个（简单的，顺序的）通用反馈传输方案，适用于一大类无记忆信道和输入分布，实现任何速率低于相应的互信息。这为最优反馈通信提供了一个统一的框架，其中Horstein方案（BSC）和Schalkwijk-Kailath方案（AWGN信道）是特例。因此，作为推论，我们证明了Horstein方案确实达到了BSC容量，解决了一个长期存在的猜想。我们还提供了封闭形式的表达式的错误概率的计划在一个范围内的速率，并得出可实现的速率在失配设置的计划是根据错误的信道模型设计的。给出了几个具体通道的后验匹配方案的示例，并对相应的误差概率表达式进行了评估。所采用的证明技术利用迭代函数系统的信息速率和收缩特性之间的新关系。
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.