New channel coding achievability bounds

Three essentially different approaches to the constructive part of the channel coding theorem have been proposed by Shannon, Feinstein and Gallager, respectively, leading to upper bounds on the minimal error probability achievable with a given rate and blocklength. Here, new upper bounds are given on both average and maximal error probability, which are tighter than existing bounds for many ranges of blocklength and channel parameters of interest. Along with converse bounds, the new achievability bounds allow to approximate tightly the maximum rate achievable for a given blocklength and error probability for blocklengths as short as n = 200 for both the BSC and the BEC.