Asymptotic weight distributions of irregular repeat-accumulate codes

In this paper, the average input-parity weight enumerator (AIPWE) of regular/irregular repeat-accumulate (RA) ensembles is derived, by viewing an RA code as a serial concatenation of an outer low-density generator matrix (LDGM) code and an inner accumulator. The exact average weight distribution (AWD) of the systematic and nonsystematic versions of the RA ensembles are then obtained from their AIPWE´s. We further derive the asymptotic growth exponent of the AWD´s, which are then used to bound the ensemble performance under maximum likelihood (ML) decoding. It is shown that simple nonsystematic regular RA ensembles outperform systematic regular RA and regular low-density parity-check (LDPC) ensembles and have distance spectrum which closely resembles that of the random ensemble.