Computing 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 from a fixed, finite-size alphabet, S a discrete-valued random variable (RV) and N a Gaussian RV. The information rate I(X; X+S+N) serves as a tight lower bound for capacity of intersymbol interference (ISI) channels corrupted by Gaussian noise. The new bounds can be calculated with a reasonable computational load and provide a similar level of tightness as the well-known conjectured lower bound by Shamai and Laroia for a good range of finite-ISI channels of practical interest. The computation of the presented bounds requires the evaluation of the magnitude sum of the precursor ISI terms as well as the identification of dominant terms among them seen at the output of the minimum mean-squared error (MMSE) decision feedback equalizer (DFE).