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We consider the discrete-time intersymbol interference (ISI) channel model,with additive Gaussian noise and fixed i.i.d. inputs. In this setting, weinvestigate the expression put forth by Shamai and Laroia as a conjecturedlower bound for the input-output mutual information after application of aMMSE-DFE receiver. A low-SNR expansion is used to prove that the conjecturedbound does not hold under general conditions, and to characterize inputs forwhich it is particularly ill-suited. One such input is used to construct acounterexample, indicating that the Shamai-Laroia expression does not alwaysbound even the achievable rate of the channel, thus excluding a naturalrelaxation of the original conjectured bound. However, this relaxed bound isthen shown to hold for any finite entropy input and ISI channel, when the SNRis sufficiently high. Finally, new simple bounds for the achievable rate areproven, and compared to other known bounds. Information-Estimation relationsand estimation-theoretic bounds play a key role in establishing our results.

Lower Bounds and Approximations for the Information Rate of the ISI Channel