Random Coding Bound for Channels with Memory - Decoding Function with Partial Overlapping. Part 2. Examples and Discussion
Introduction: Suboptimal random coding exponent Er*(R; ) for a wide class of finite-state channel models using a mismatched decoding function φ was obtained and presented in the first part ofthis work. We used  function represented as a product of a posteriori probabilities of non-overlapped input subblocks of length 2B+1 relative to the overlapped output subblocks of length 2W+1. It has been shown that the computation of function Er* (R; ) is reduced to the calculation of the largest eigenvalue of a square non-negative matrix of an order depending on the B and W values. Purpose: To illustrate the approach developed in the first part of this study with its application to various channel modelled as a probabilistic finite-state machine. Results: We consider channels with state transitions not depending on the input symbol (channels with freely evolving states), and channels with deterministic state transitions, in particular, intersymbol interference channels. We present and discuss numerical results of calculating this random coding exponent in a full range of code rates for some of channel models for which similar results were not obtained before. Practical computations were carried out for relatively small values of B and W. Nevertheless, even for small values of these parameters a good correspondence with some known results for optimal decoding was shown.