Accumulate-repeat-accumulate-accumulate-codes

Inspired by recently proposed accumulate-repeat-accumulate (ARA) codes (Abbasfar et al. (2004)), in this paper we propose a channel coding scheme called accumulate-repeat-accumulate-accumulate (ARAA) codes. These codes can he seen as serial turbo-like codes or as a subclass of low density parity check (LDPC) codes, and they have a projected graph or protograph representation, this allows for a high-speed iterative decoder implementation using belief propagation. An ARAA code can be viewed as a precoded repeat-and-accumulate (RA) code with puncturing in concatenation with another accumulator, where simply an accumulator is chosen as the precoder; thus ARAA codes have a very fast encoder structure. Using density evolution on their associated protographs, we find examples of rate-1/2 ARAA codes with maximum variable node degree 4 for which a minimum bit-SNR as low as 0.21 dB from the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA or irregular RA (IRA) or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore by puncturing the accumulators we can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results show comparable performance with the best-known LDPC codes but with very low error floor even at moderate block sizes.