On Zero-Rate Error Exponents of Finite-State Channels With Input-Dependent States

We derive a single-letter formula for the zero-rate reliability (error exponent) of a finite-state channel whose state variable depends deterministically (and recursively) on past channel inputs, where the code complies with a given channel input constraint. Special attention is then devoted to the important special case of the Gaussian channel with intersymbol interference, where more explicit results are obtained.