Easily Computed Lower Bounds on the Information Rate of Intersymbol Interference Channels

TL;DR

This paper introduces easily computable lower bounds on the information rate of intersymbol interference channels, providing tight estimates that outperform previous bounds at high SNRs.

Contribution

The authors propose a new method to compute lower bounds on the information rate for ISI channels, which are both tight and computationally efficient.

Findings

Bounds are comparable to the conjectured lower bound by Shamai and Laroia.

New bounds are tighter at high SNRs.

Method involves a mismatched mutual information function and simple integrations.

Abstract

Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well known that with S representing the precursor intersymbol interference (ISI) at the decision feedback equalizer (DFE) output, I(X; X+S+N) serves as a tight lower bound for the symmetric information rate (SIR) as well as capacity of the ISI channel corrupted by Gaussian noise. When evaluated on a number of well-known finite-ISI channels, these new bounds provide a very similar level of tightness against the SIR to the conjectured lower bound by Shamai and Laroia at all signal-to-noise ratio (SNR) ranges, while being actually tighter when viewed closed up at high SNRs. The new lower bounds are obtained in two steps: First, a "mismatched" mutual information function is introduced which can be proved as a lower bound to I(X; X+S+N). Secondly, this function is further bounded from below by an expression that can be computed easily via a few single-dimensional integrations with a small computational load.