Spatially Coupled Turbo Codes: Principles and Finite Length Performance

TL;DR

This paper reviews spatially coupled turbo codes, focusing on their principles, density evolution analysis, and finite length performance, demonstrating threshold saturation and near-Shannon limit thresholds as coupling increases.

Contribution

It introduces a detailed overview of spatially coupled turbo codes, including their construction, analysis, and finite length performance, highlighting threshold saturation effects.

Findings

BP threshold approaches Shannon limit with increased coupling

Threshold saturation observed for all code rates

Finite length simulations confirm theoretical predictions

Abstract

In this paper, we give an overview of spatially coupled turbo codes (SC-TCs), the spatial coupling of parallel and serially concatenated convolutional codes, recently introduced by the authors. For presentation purposes, we focus on spatially coupled serially concatenated codes (SC-SCCs). We review the main principles of SC-TCs and discuss their exact density evolution (DE) analysis on the binary erasure channel. We also consider the construction of a family of rate-compatible SC-SCCs with simple 4-state component encoders. For all considered code rates, threshold saturation of the belief propagation (BP) to the maximum a posteriori threshold of the uncoupled ensemble is demonstrated, and it is shown that the BP threshold approaches the Shannon limit as the coupling memory increases. Finally we give some simulation results for finite lengths.