A comparison of known codes, random codes, and the best codes

Abstract

This paper calculates new bounds on the size of the performance gap between random codes and the best possible codes on the binary symmetric channel (BSC), binary erasure channel (BEC), and the additive white Gaussian noise (AWGN) channel. The paper also presents substantial numerical evaluation of the performance of random codes and existing standard lower bounds for the BEC, BSC, and the AWGN channel. These results provide a useful standard against which to measure many popular codes including turbo codes, e.g., there exist turbo codes that perform within 0.6 dB of the bounds over a wide range of block lengths.