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A Posterior Matching Scheme for Finite-State Channels with Feedback
 

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

  

Source: Anastasopoulos, Achilleas - Department of Electrical Engineering and Computer Science, University of Michigan

 

Collections: Engineering; Computer Technologies and Information Sciences