Maximum likelihood decoding analysis of accumulate-repeat-accumulate codes

Repeat-Accumulate (RA) codes are the simplest turbo-like codes that achieve good performance. However, they cannot compete with Turbo codes or low-density parity-check codes (LDPC) as far as performance is concerned. The Accumulate-Repeat-Accumulate (ARA) codes, as a subclass of LDPC codes, are obtained by adding a pre-coder in front of the RA codes with puncturing, where an accumulator is chosen as the precoder. These codes not only are very simple, but also achieve excellent performance with iterative decoding. In this paper, the performance of these codes with maximum likelihood (ML) decoding are analyzed and compared to the random codes by very tight bounds. The weight distributions of some simple ARA codes are obtained, and through existing tightest bounds we have shown that the ML SNR thresholds of the ARA codes approach very closely to the performance of random codes. We have shown that the use of a precoder improves the SNR threshold but the interleaving gain remains unchanged with respect to the RA codes with puncturing.