RA Codes Achieve AWGN Channel Capacity

Abstract

In ref. [3] we introduced a simplified ensemble of serially concatenated “turbo-like” codes which we called repeat-accumulate, or RA codes. These codes are very easy to decode using an iterative decoding algorithm derived from belief propagation on the appropriate Tanner graph, yet their performance is scarcely inferior to that of full-fledged turbo codes. In this paper, we prove that on the AWGN channel, RA codes have the potential for achieving channel capacity. That is, as the rate of the RA code approaches zero, the average required bit E_b/N_0 for arbitrarily small error probability with maximum-likelihood decoding approaches log 2, which is the Shannon limit. In view of the extreme simplicity of RA codes, this result is both surprising and suggestive.