Complexity-Performance Tradeoff for Intersymbol Interference Channels—Random Coding Analysis

In this work, we look at symmetric cutoff rates for intersymbol interference (ISI) channels with additive white Gaussian noise (AWGN), as well as with colored noise. The derived symmetric cutoff rates are used to estimate the signal-to-noise ratio (SNR) losses expected over channels with various reduced complexity channels. The techniques used in this work are generalizations on established approaches to computing the cutoff rate for linear ISI channels. The generalizations mentioned consist of an extension to traditional schemes by considering: (a) general (e.g., nonlinear) ISI; (b) colored Gaussian noise; and (c) suboptimal decoding approaches (reduced number of trellis states). Examples involving some real ISI channels are examined and the performance differences of real LDPC coded channels are compared with the results obtained via the symmetric cutoff rate analysis.