A Sphere-Packing Exponent for Mismatched Decoding

We derive a sphere-packing error exponent for mismatched decoding over discrete memoryless channels. We find a lower bound to the probability of error of mismatched decoding that decays exponentially for coding rates smaller than a new upper bound to the mismatch capacity. For rates higher than the new upper bound, the error probability is shown to be bounded away from zero. The new upper bound is shown to improve over previous upper bounds to the mismatch capacity.