# Gaussian Intersymbol Interference Channels With Mismatch

## TL;DR

This paper derives computable lower bounds for the mismatch capacity of Gaussian ISI channels with incorrect impulse response assumptions, providing insights into achievable rates and decoding performance under mismatch conditions.

## Contribution

It introduces single-letter lower bounds for mismatch capacity and analyzes their behavior, advancing understanding of decoding with channel model mismatch.

## Key findings

- Derived single-letter lower bounds for mismatch capacity
- Demonstrated non-trivial behavior of achievable rates with mismatch parameters
- Established the random coding exponent for mismatched decoders assuming no ISI

## Abstract

This paper considers the problem of channel coding over Gaussian intersymbol interference (ISI) channels with a given metric decoding rule. Specifically, it is assumed that the mismatched decoder has an incorrect assumption on the impulse response function. The mismatch capacity is the highest achievable rate for a given decoding rule. Existing lower bounds to the mismatch capacity for channels and decoding metrics with memory (as in our model) are presented only in the form of multi-letter expressions that have not been calculated in practice. Consequently, they provide little insight on the mismatch problem. In this paper, we derive computable single-letter lower bounds to the mismatch capacity, and discuss some implications of our results. Our achievable rates are based on two ensembles, the ensemble of codewords generated by an autoregressive process, and the ensemble of codewords drawn uniformly over a "type class" of real-valued sequences. Computation of our achievable rates demonstrates non-trivial behavior of the achievable rates as a function of the mismatched parameters. As a simple application of our technique, we derive also the random coding exponent associated with a mismatched decoder which assumes that there is no ISI at all. Finally, we compare our results with universal decoders which are designed outside the true class of channels that we consider in this paper.