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 inter-symbol interference (ISI), where more explicit results are obtained. 
Neri Merhav
cs.IT math.IT