Threshold Saturation for Spatially Coupled Turbo-like Codes over the Binary Erasure Channel

TL;DR

This paper proves threshold saturation for spatially coupled turbo-like codes over the binary erasure channel by introducing a simplified graph representation and applying potential function analysis.

Contribution

It introduces a compact graph representation for SC-TC and BCC ensembles and applies scalar admissible system analysis to prove threshold saturation.

Findings

Threshold saturation is proven for SC-TC and BCC over BEC.

A new graph representation simplifies code analysis.

Application of potential functions confirms threshold saturation.

Abstract

In this paper we prove threshold saturation for spatially coupled turbo codes (SC-TCs) and braided convolutional codes (BCCs) over the binary erasure channel. We introduce a compact graph representation for the ensembles of SC-TC and BCC codes which simplifies their description and the analysis of the message passing decoding. We demonstrate that by few assumptions in the ensembles of these codes, it is possible to rewrite their vector recursions in a form which places these ensembles under the category of scalar admissible systems. This allows us to define potential functions and prove threshold saturation using the proof technique introduced by Yedla et al..