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

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.