On trapping sets for repeat accumulate accumulate codes

The serial concatenation of a repetition code with two or more accumulators has the advantage of a simple encoder structure. Furthermore, the resulting ensemble is asymptotically good and exhibits minimum distance growing linearly with block length. For low-density parity-check codes, the notion of trapping sets has been introduced to estimate the performance of these codes under non-maximum likelihood decoding. We briefly address asymptotic expressions for the normalized minimum trapping distance for the Gallager-Zyablov-Pinsker bit flipping decoding algorithm. Then we consider belief propagation decoding and present a closed form finite length ensemble average trapping set enumerator for repeat accumulate accumulate codes by creating a trellis representation of trapping sets. For this case, we also obtain asymptotic expressions and evaluate them numerically.