Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles

TL;DR

This paper introduces a method to enumerate trapping sets in repeat multiple accumulate codes, aiding the analysis of their iterative decoding performance.

Contribution

It presents a closed-form finite length trapping set enumerator for repeat multiple accumulate codes using a trellis representation.

Findings

Provides a finite length ensemble trapping set enumerator

Derives asymptotic expressions for large block lengths

Numerical evaluation of trapping set distributions

Abstract

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. However, in practice these codes cannot be decoded by a maximum likelihood decoder, and iterative decoding schemes must be employed. For low-density parity-check codes, the notion of trapping sets has been introduced to estimate the performance of these codes under iterative message passing decoding. In this paper, we present a closed form finite length ensemble trapping set enumerator for repeat multiple accumulate codes by creating a trellis representation of trapping sets. We also obtain the asymptotic expressions when the block length tends to infinity and evaluate them numerically.