{'fraction_non_alphanumeric': 0.03508771929824561, 'fraction_numerical': 0.0, 'mean_word_length': 5.111111111111111, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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.