Ordering Finite-State Markov Channels by Mutual Information

TL;DR

This paper extends an ordering result from symbolwise error probability to mutual information for Markov channels, enabling capacity comparisons and simplifying analysis of channels with different states.

Contribution

It introduces an ordering of Markov channels based on mutual information, applicable when the capacity-achieving input is iid, aiding in channel capacity analysis.

Findings

Channels can be ordered by mutual information.

The ordering simplifies capacity analysis for complex channels.

Applicable to channels with iid capacity-achieving inputs.

Abstract

In previous work, an ordering result was given for the symbolwise probability of error using general Markov channels, under iterative decoding of LDPC codes. In this paper, the ordering result is extended to mutual information, under the assumption of an iid input distribution. For certain channels, in which the capacity-achieving input distribution is iid, this allows ordering of the channels by capacity. The complexity of analyzing general Markov channels is mitigated by this ordering, since it is possible to immediately determine that a wide class of channels, with different numbers of states, has a smaller mutual information than a given channel.