Generalized Spatially Coupled Parallel Concatenated Convolutional Codes With Partial Repetition

TL;DR

This paper introduces generalized spatially coupled turbo-like codes with partial repetition, demonstrating improved decoding thresholds and capacity-approaching performance as the repetition factor increases.

Contribution

It extends existing spatially coupled codes by incorporating partial repetition, deriving density evolution equations, and analyzing their asymptotic capacity-approaching behavior.

Findings

Decoding thresholds improve with higher repetition factor q.

Codes exhibit threshold saturation property.

As q approaches infinity, codes asymptotically reach channel capacity.

Abstract

We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the PCC encoding. GSC-PCCs can be seen as a generalization of the original spatially coupled parallel concatenated convolutional codes (SC-PCCs) proposed by Moloudi et al. [1]. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. We show that the proposed codes have some nice properties such as threshold saturation and that their decoding thresholds improve with the repetition factor $q$. Most notably, our analysis suggests that the proposed codes asymptotically approach the capacity as $q$ tends to infinity with any given constituent convolutional code.