| | |
Summary: 1
A Posterior Matching Scheme for Finite-State
Channels with Feedback
Jung Hyun Bae and Achilleas Anastasopoulos
Electrical Engineering and Computer Science Department
University of Michigan
Ann Arbor, MI, 48109-2122
email: {jungbae, anastas}@umich.edu
Abstract
For a memoryless channel, although feedback cannot increase capacity, it can reduce the complexity
and/or improve the error performance of a communication system. Recently, Shayevitz and Feder
proposed the posterior matching scheme (PMS) which is a simple recursive transmission scheme
that achieves the capacity of memoryless channels with feedback. Furthermore, Coleman provided a
Lyapunov function approach to prove capacity achievability of the PMS.
In this paper, we investigate a capacity-achieving PMS for the case of finite-state channels (FSCs).
We first derive a single-letter expression for the capacity of the FSC with delayed output and state
feedback by formulating the problem in a stochastic control framework. The resulting capacity ex-
pression can be evaluated using dynamic programming. We then propose a simple recursive PMS-like
transmission scheme. To prove capacity achievability of the proposed PMS, we identify an appropriate
Markov chain induced by the PMS, and modify Coleman's Lyapunov function approach to prove the
|
