  Exponential error bounds for the finite-alphabet interference channel (IFC)
with two transmitter-receiver pairs, are investigated under the random coding
regime. Our focus is on optimum decoding, as opposed to heuristic decoding
rules that have been used in previous works, like joint typicality decoding,
decoding based on interference cancellation, and decoding that considers the
interference as additional noise. Indeed, the fact that the actual interfering
signal is a codeword and not an i.i.d. noise process complicates the
application of conventional techniques to the performance analysis of the
optimum decoder. Using analytical tools rooted in statistical physics, we
derive a single letter expression for error exponents achievable under optimum
decoding and demonstrate strict improvement over error exponents obtainable
using suboptimal decoding rules, but which are amenable to more conventional
analysis.
