On zero-rate error exponents of finite-state channels with input-dependent states

TL;DR

This paper derives a formula for the zero-rate error exponent of finite-state channels with input-dependent states, including a detailed analysis of Gaussian channels with inter-symbol interference, advancing understanding of channel reliability.

Contribution

It provides a single-letter formula for the zero-rate error exponent of finite-state channels with input-dependent states, including explicit results for Gaussian channels with ISI.

Findings

Derived a single-letter formula for zero-rate error exponents.

Provided explicit results for Gaussian channels with ISI.

Enhanced understanding of reliability limits in channels with input-dependent states.

Abstract

We derive a single-letter formula for the zero-rate reliability (error exponent) of a finite-state channel whose state variable depends deterministically (and recursively) on past channel inputs, where the code complies with a given channel input constraint. Special attention is then devoted to the important special case of the Gaussian channel with inter-symbol interference (ISI), where more explicit results are obtained.