Evaluation of Gallager Codes for Short Block Length and High Rate Applications

Gallager codes with large block length and low rate (e.g., N ≃ 10,000–40,000, R ≃ 0.25–0.5) have been shown to have record-breaking performance for low signal-to-noise applications. In this paper we study Gallager codes at the other end of the spectrum. We first explore the theoretical properties of binary Gallager codes with very high rates and observe that Gallager codes of any rate offer runlength-limiting properties at no additional cost.We then report the empirical performance of high rate binary and non-binary Gallager codes on three channels: the binary input Gaussian channel, the binary symmetric channel, and the 16-ary symmetric channel.We find that Gallager codes with rate R = 8/9 and block length N = 1998 bits outperform comparable BCH and Reed-Solomon codes (decoded by a hard input decoder) by more than a decibel on the Gaussian channel.