An information theoretic study of reduced-complexity receivers for intersymbol interference channels

Abstract

The complexity of the optimal receiver for communications over a discrete-time additive Gaussian intersymbol interference channel typically grows exponentially with the duration of the channel impulse response. Consequently, practical sub-optimal receivers are often designed as though the channel impulse response were shorter than it is. While previous studies on the performance of such receivers have mainly focused on bit error rates in uncoded systems, this thesis takes a different approach to the problem. We adopt an information theoretic approach and study the rates that are achievable in the Shannon sense over the true channel with the given, possibly sub-optimal, decoding rule. One can establish that, under such mismatch conditions, the achievable rates are bounded in the Signal-to-Noise Ratio necessitating the use of a linear equalizer at the front end of the decoder. We derive the achievable rates for these schemes and optimize under complexity constraints the design of the equalizer and the receiver. Overall, two ensemble of codes are considered: the Independent Identically Distributed Gaussian ensemble and the "spherical" ensemble, where codewords are uniformly distributed over a sphere.