A complex-integration approach to the saddlepoint approximation for random-coding bounds

Abstract

This paper derives a saddlepoint approximation for the random-coding bound to the error probability of channel coding by using complex-integration techniques. The approximation is given by a sum of two terms: one with Gallager’s exponent, and a second one with Arimoto’s strong converse exponent (above capacity) or the sphere-packing exponent (below the critical rate).