New channel coding achievability bounds
Abstract
Three essentially different approaches to the constructive part of the听 channel 听 coding 听theorem have been proposed by Shannon, Feinstein and Gallager, respectively, leading to upper听 bounds 听on the minimal error probability achievable with a given rate and blocklength. Here,听 new 听upper听 bounds 听are given on both average and maximal error probability, which are tighter than existing听 bounds 听for many ranges of blocklength and听 channel 听parameters of interest. Along with converse听 bounds , the听 new achievability 听 bounds 听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.