Random - Coding Bounds for Threshold Decoders: Error Exponent and Saddlepoint Approximation
Recently, spurred by the construction of near-capacity-achieving codes, renewed attention has been paid to the error probability in the finite-length regime. This paper considers random-coding bounds to the decoding error probability with threshold decoders. A slightly improved version of the dependence-testing bound is derived. A loosening of this bound generates a family of Feinsteinlike bounds, which improve on Feinstein's original version. The error exponents of these bounds are determined and simple, yet accurate, saddle-point approximations to the corresponding error probabilities are derived.