A survey of three-dimensional turbo codes and recent performance enhancements
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RESEARCH
Open Access
A survey of three-dimensional turbo codes and recent performance enhancements Dhouha Kbaier Ben Ismail1,2*, Catherine Douillard1,2 and Sylvie Kerouédan1,2
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. Keyword: Turbo code, Iterative decoding, Three-dimensional turbo code, Convergence threshold, EXIT chart, Time-varying trellis, Irregular turbo code, Degree profile, Dijkstra's algorithm, Correlation graph
1. 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… Coding theorist professors had begotten more coding theory Ph.D.'s in their own image… no one else cared; it was time to see this perversion for what it was. Give up this fantasy and take up a useful occupation… Coding is dead.” This assertion was contradicted 20 years later by the invention of turbo codes (TCs) [1], which was a revival for the channel coding research community. Their near-capacity performance and their suitability for practical implementation explain the adoption of TCs in various communication standards as early as the late 1990s. However, TCs suffer from a flattening effect when the error rate reaches a limit and stops improving. In future system generations, low error rates will be required to open the way to real* Correspondence: [email protected] 1 Institut Telecom, Telecom Bretagne, UMR CNRS 3192 Lab-STICC, Technopôle Brest Iroise, CS 83818, Brest Cedex 3 29238, France 2 Université européenne de Bretagne, Bretagne 35000, France
time and demanding applications, such as TV broadcasting or videoconferencing. The minimum Hamming distance (MHD) of state-of-the-art TCs may not be sufficient
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