Analysis of three-dimensional turbo codes (original) (raw)
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A survey of three-dimensional turbo codes and recent performance enhancements
2013
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.
Reducing the convergence loss of 3-dimensional turbo codes
2010 6th International Symposium on Turbo Codes & Iterative Information Processing, 2010
This paper deals with the convergence loss reduction of a 3-dimensional turbo code combining both parallel and serial concatenation. This code is derived from the classical turbo code by concatenating a rate-l post-encoder at its output. In order to reduce the observable loss of convergence at high error rates, we propose first a time varying construction of the post-encoded parity. Then, we analyse the association of the 3-dimensional turbo code with high order modulations, where both the systematic bits and the post-encoded parity bits are more protected than the other parity bits. Performance comparisons are made between the 3GPP2 standardized turbo code and the 3dimensional 3GPP2 turbo code. The different stages are illustrated with simulation results, asymptotical bounds and EXIT charts.
Improving 3-dimensional turbo codes using 3GPP2 interleavers
2009 First International Conference on Communications and Networking, 2009
This paper deals with the performance improvement of a 3-dimensional turbo code based on the partial concatenation of the 3GPP2 code with a rate-1 post-encoder. First, we optimize the distance spectrum of the 3-dimensional 3GPP2 turbo code by means of the adoption of a non regular post-encoding pattern. This allows us to increase the minimum Hamming distance and thereby to improve the performance at very low error rates. Then, we propose a time varying construction of the postencoded parity in order to reduce the observable loss of convergence at high error rates. The different improvement stages are illustrated with simulation results, asymptotical bounds and EXIT charts.
IEEE Transactions on Communications, 2009
Thanks to the probabilistic message passing performed between its component decoders, a turbo decoder is able to provide strong error correction close to the theoretical limit. However, the minimum Hamming distance (min) of a turbo code may not be sufficiently large to ensure large asymptotic gains at very low error rates (the so-called flattening effect). Increasing the min of a turbo code may involve using component encoders with a large number of states, devising more sophisticated internal permutations, or increasing the number of component encoders. This paper addresses the latter option and proposes a modified turbo code in which a fraction of the parity bits are encoded by a rate-1, third encoder. The result is a noticeably increased min, which improves turbo decoder performance at low error rates. Performance comparisons with turbo codes and serially concatenated convolutional codes are given.
Adding a rate-1 third dimension to turbo codes
2007
Thanks to the message passing principle, turbo decoding is able to provide strong error correction near the theoretical (Shannon) limit. However, the minimum Hamming distance (MHD) of a Turbo Code may not be sufficient to prevent a detrimental change in the error rate vs. signal to noise ratio curve, the so-called flattening. Increasing the MHD of a Turbo Code may involve using component encoders with a large number of states, devising more sophisticated internal permutations, or increasing the dimension of the Turbo Code, i.e. the number of component encoders. This paper addresses the latter option and proposes a modified Turbo Code, in which some of the parity bits stemming from the classical component encoders are encoded by a rate-1, third encoder. The result is a significantly increased MHD, which improves turbo decoder performance at low error rates, at the expense of a very small increase in complexity. In the paper, we compare the performance of the proposed Turbo Code with that of the DVB-RCS Turbo Code and the DVB-S2 LDPC code.
Parity concatenated turbo codes: study of their structure and performance bounds
Eighth IEEE International Symposium on Spread Spectrum Techniques and Applications - Programme and Book of Abstracts (IEEE Cat. No.04TH8738), 2004
Recently, turbo coding schemes involving block codes have been studied, significantly augmenting its overall performance. Usually, a turbo code uses different sets of parity information for the same set of information bits. In this paper we investigate the usage of a turbo scheme using two different sets of information bits, each encoded by separate constituent block coders. Their encoded bits are then linked by a simple module-2 sum, originating an extra amount of parity bits. The overall code can be seen as a turbo code, yielding enhanced performance at an expense of a small increase in complexity, since few decoding iterations are required to obtain good results. Using these turbo schemes it is possible to obtain codes with low coding rate, which makes them especially suitable for spread spectrum systems where they can be used for achieving simultaneously error correction and bandwidth expansion.
Bit Error Rate Performance of Third Generation Turbo Codes
2005
After the invention of Turbo Codes (TCs) many coding theorist and researchers further tried to improve the performance of these codes. Now the performance of Turbo Codes is becoming closer to the Shannon's limit. The performance of turbo codes depends on its architectural component and the architecture of TCs is application dependent. So the researchers are trying to develop the standard architecture of TCs for specific application so that its performance becomes optimum. In this paper we analyze the performance, in terms of bit error rate (BER) vs. bit energy to noise spectral ratio (E b /N o ) of Turbo Codes that are using in Third Generation Partnership Project standard (Universal Mobile Telephone Systems-UMTS) . This paper focuses on the effect of the variation of the architectural components of UMTS TCs on its performance. In particular code rate, frame size i.e., length of information bits, number of decoding iteration and channel models variations of Turbo Codes are taken into account in studying the performance of Turbo Codes. These effects are shown in the performance curve (BER vs. E b /N 0 ) of the UMTS standard turbo codes.
Convergence Analysis of Turbo Decoding of Serially Concatenated Block Codes and Product Codes
EURASIP Journal on Advances in Signal Processing, 2005
The geometric interpretation of turbo decoding has founded a framework, and provided tools for the analysis of parallelconcatenated codes decoding. In this paper, we extend this analytical basis for the decoding of serially concatenated codes, and focus on serially concatenated product codes (SCPC) (i.e., product codes with checks on checks). For this case, at least one of the component (i.e., rows/columns) decoders should calculate the extrinsic information not only for the information bits, but also for the check bits. We refer to such a component decoder as a serial decoding module (SDM). We extend the framework accordingly and derive the update equations for a general turbo decoder of SCPC and the expressions for the main analysis tools: the Jacobian and stability matrices. We explore the stability of the SDM. Specifically, for high SNR, we prove that the maximal eigenvalue of the SDM's stability matrix approaches d − 1, where d is the minimum Hamming distance of the component code. Hence, for practical codes, the SDM is unstable. Further, we analyze the two turbo decoding schemes, proposed by Benedetto and Pyndiah, by deriving the corresponding update equations and by demonstrating the structure of their stability matrices for the repetition code and an SCPC code with 2 × 2 information bits. Simulation results for the Hamming [(7, 4, 3)] 2 and Golay [(24, 12, 8)] 2 codes are presented, analyzed, and compared to the theoretical results and to simulations of turbo decoding of parallel concatenation of the same codes.
Performance analysis and optimization of concatenated block-turbo coding schemes
Communications, 2004
In this paper, a concatenated coding scheme consisting of an outer algebraic block code performing hard decoding connected to an inner turbo code through a rectangular interleaver is analyzed. The performance of the concatenated code is evaluated through a semi-analytical approach, based on the expression of the word error probability at the output of the outer decoder as a function of the error statistics at the output of the turbo decoder estimated through simulation. The proposed technique yields results that depend on the size of the interleaver, and permits to obtain trade-offs between that size and the outer code characteristics.