The intersymbol interference channel: lower bounds on capacity and channel precoding loss

The discrete-time additive Gaussian intersymbol interference (ISI) channel with i.i.d. (not necessarily Gaussian) input signals is considered. Several new and old lower bounds on the capacity are derived in a unified manner by assuming different front-end receiver filters, in particular the sampled whitened matched filter (SWMF) and the minimum mean-squared error-decision feedback equalizer (MMSE-DFE) filter. The features of the bounds are demonstrated and compared in several examples with binary and quaternary input signals. It is also shown that the effect of an ideal post-cursor or tail cancellation, in an information-preserving context, depends primarily on the front-end filter. While, as is well known, ideal post-cursor cancellation at the output of the SWMF decreases the information, the opposite trend is seen when an MMSE-DFE front filter is considered. This observation reflects the basic theoretical obstacles in precoding, i.e., ideal post-cursor cancellation in the presence of a pre-cursor. It is used to assess the inherent loss (in terms of information rates as compared to the rates achievable with the hypothetical ideal post-cursor cancellation) associated with any post-cursor cancellation technique such as precoding, DFE, or other variants, when operating in synergy with the MMSE-DFE front-end filter. The effect of the front-end filter on an ideally interleaved, precoded coded-modulation system is also addressed.