On the minimum trapping distance of repeat accumulate accumulate codes

Abstract

We consider the ensemble of codes formed by a serial concatenation of a repetition code with two accumulators through uniform random interleavers. For this ensemble, asymptotic expressions for the normalized minimum trapping distance are derived. We employ a variant of the Gallager-Zyablov-Pinsker bit flipping decoding algorithm on a binary symmetric channel, where the analysis is based on the factor graph of the code. In particular, we show that the minimum trapping distance can be determined by solving a non-linear optimization problem. As a result we find that the minimum trapping distance grows linearly with block length for code rates of 1/3 and smaller, albeit with very small growth rate coefficients.