Performance bound for maximum-likelihood reception of digital data

Maximum-likelihood sequence estimation (MLSE) of data sequences is considered as an approach to increasing data rates over band-limited channels, such as exist in analog telephone facilities. Analytical prediction of the efficacy of MLSE for specific channels had been viewed as intractable until Forney gave a formula for an asymptotic upper bound on the probability of symbol errorp. Forney's bound involved an infinite series, and letting the noise power No --} 0, he chose the asymptotically largest series term as an asymptotic bound onp, ignoring a very basic perplexing open question: How do we know the bounding series is not identically infinity for allN_0 → 0?We show that under very general conditions Forney's bounding series converges for a nontrivial intervalN_0 > 0. As a corollary, we prove Forney's aforementioned asymptotic formula forp. The analysis includes the class of channels with spectral nulls, since band edge nulls can be associated with telephone channels that are pulsed at high rates.