A survey of three-dimensional turbo codes and recent performance enhancements

Dhouha Kbaier Ben Ismail,Sylvie Kerouédan,Catherine Douillard

doi:10.1186/1687-1499-2013-115

Abstract

This paper presents a survey of two techniques intended for improving the performance of conventional turbo codes (TCs). The first part of this work is dedicated to explore a hybrid concatenation structure combining both parallel and serial concatenation based on a three-dimensional (3D) code. The 3D structure, recently introduced by Berrou et al., is able to ensure large asymptotic gains at very low error rates at the expense of an increase in complexity and a loss in the convergence threshold. In order to reduce the loss in the convergence threshold, the authors consider first a time-varying construction of the post-encoded parity. Then, they investigate the association of the 3D TC with high-order modulations according to the bit-interleaved coded modulation approach. The second part of this study deals with irregular TCs. In contrast to 3D TCs, although irregular TCs can achieve performance closer to capacity, their asymptotic performance is very poor. Therefore, the authors propose irregular turbo coding schemes with suitable interleavers in order to improve their distance properties. Finally, a modified encoding procedure, inspired from the 3D TC, makes it possible to obtain irregular TCs which perform better than the corresponding regular codes in both the waterfall and the error floor regions.

Highlights

In 1971, the whole community of coding and information theory was in phase with the famous speech of Professor Robert McEliece: “Too many equations had been generated with too few consequences
The association of irregular turbo codes (TCs) with the same post-encoder used for 3D TCs results in irregular turbo coding schemes which perform better than regular TCs at low and high signal-to-noise ratios (SNRs) at the same time
We have investigated a simple time-varying post-encoder in order to increase locally its minimum distance. This improves the level of the extrinsic information provided by the predecoder to the two soft-input soft-output (SISO) decoders, which reduces the loss of convergence threshold for 3D TCs

Summary

Introduction

In 1971, the whole community of coding and information theory was in phase with the famous speech of Professor Robert McEliece: “Too many equations had been generated with too few consequences. In [2,3], a three-dimensional (3D) TC was introduced, combining both parallel and serial concatenation It is derived from the classical TC by concatenating a rate-1 postencoder at its output, which encodes only a fraction λ of the parity bits from the upper and lower constituent encoders. The authors investigate this hybrid concatenated coding scheme. Afterwards, their interests go towards irregular TCs [4]. We discuss convergence issues in the same section and introduce time-varying three-dimensional TCs as an alternative to reduce the loss in the convergence threshold. The association of irregular TCs with the same post-encoder used for 3D TCs results in irregular turbo coding schemes which perform better than regular TCs at low and high signal-to-noise ratios (SNRs) at the same time.

Properties of three-dimensional turbo codes

Example 1

Example 2

Irregular turbo codes

Findings

Conclusions