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Fast convergencealgorithm forLDPC Codes

Norbert Wehn

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Low-Density Parity-Check (LDPC)codesareone ofthemostpowerful codesknowntoday. Theyaredecoded iteratively bya messagepassing algorithm. Thereexist many different update schemes oftheexchanged messages. Themajor difference ofallupdate schemes istheconvergence speed, i.e. the achieved communications performance foralimited numberof iterations. Thispaperpresents anewdecoding algorithm whichefficiently utilizes theencoder property oflinear encodable LDPC codes. Thebasic ideaistointerpret theLDPC encoder asanencoder withpuncturing unitwhichopensaswellthedoorforhybrid ARQ schemes. Thepresented newdecoding algorithm showsa faster convergence behavior thanstate ofartdecoding schemes anditresults inalowererrorfloor.

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•Jan 1, 2008•3 citations
Low-Density Parity-Check (LDPC)codesareone ofthemostpowerful codesknowntoday. Theyaredecoded iteratively bya messagepassing algorithm. Thereexist many different update schemes oftheexchanged messages. Themajor difference ofallupdate schemes istheconvergence speed, i.e. the achieved communications performance foralimited numberof iterations. Thispaperpresents anewdecoding algorithm whichefficiently utilizes theencoder property oflinear encodable LDPC codes. Thebasic ideaistointerpret theLDPC encoder asanencoder withpuncturing unitwhichopensaswellthedoorforhybrid ARQ schemes. Thepresented newdecoding algorithm showsa faster convergence behavior thanstate ofartdecoding schemes anditresults inalowererrorfloor.
Low-density parity-check (LDPC) codes are one of the most powerful codes known today. They are decoded iteratively by a message passing algorithm. There exist many different update schemes of the exchanged messages. The major difference of all update schemes is the convergence speed, i.e. the achieved communications performance for a limited number of iterations. This paper presents a new decoding algorithm which efficiently utilizes the encoder property of linear encodable LDPC codes. The basic idea is to interpret the LDPC encoder as an encoder with puncturing unit which opens as well the door for hybrid ARQ schemes. The presented new decoding algorithm shows a faster convergence behavior than state of art decoding schemes and it results in a lower error floor
Abstract: In this paper, a fast-convergence algorithm is proposed for the decoding of low-density parity-check (LDPC) codes. By putting more weight on the message update from check node to variable node in current iteration, the proposed method speeds up the decoding significantly. Simulation results show that compared with the standard layered min-sum decoding algorithm, the proposed scheme may reduce about 1/6 iteration numbers for LDPC codes used in DVB-S2, with hardware complexity overhead less than 2%. Key–Words: LDPC code, fast convergence decoding algorithm, layered decoding, min-sum algorithm, hardware implementation 1
Recently introduced Fair-Density Parity-Check (FDPC) codes, targeting high-rate applications, offer superior error-correction performance (ECP) compared to 5G Low-Density Parity-Check (LDPC) codes, given the same number of message-passing decoding iterations. In this paper, we present a novel construction method for FDPC codes, introduce a generalization of these codes, and propose a low-complexity encoding algorithm. Numerical results demonstrate the fast convergence of the message-passing decoder for FDPC codes.
We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution (DE), a numerical method for analyzing the behavior of iterative decoding convergence of a LDPC code. We have used the method of [16] for designing of a LDPC code with optimal rate. This has been done for a given parity check node degree distribution, erasure probability and specified DE constraint. The fast behavior of DE and found optimal rate with this method compare with the previous DE constraint.
Low-density parity-check (LDPC) codes have received significant attention due to their near-Shannon-limit error performance. The belief propagation (BP) algorithm is the best-known decoding algorithm for LDPC codes. However it often needs several tens or hundreds of iterations to converge. Although fast convergence BP algorithms have been proposed, there is neither an easy tool to analyze their performance nor a standard VLSI architecture to implement them. Moreover, there exists a trade-off between waterfall (i.e., threshold) and error floor (i.e., minimum pseudo distance) performances for LDPC codes. For generalized LDPC (GLDPC) codes, better minimum distance properties can be achieved but at the expense of a rate loss. This research investigates performance analysis and hardware implementation of LDPC codes using fast convergence algorithms. Closed-form extrinsic mutual information transfer (EXIT) functions for several fast convergence BP decoding algorithms are proposed. It is shown theoretically that these algorithms converge faster than standard BP, while the corresponding thresholds remain unchanged. Since these algorithms are of serial nature, their parallelization without compromising convergence speed and error performance is also investigated. This result is useful in hardware implementation because in practice partly parallel decoding schemes are often used. This result also sheds some light on how to group nodes in order to preserve performance. The VLSI architecture of a particular decoding algorithm for LDPC codes is proposed. This approach can be adopted in many standards to achieve a large throughput. Doubly GLDPC (DGLDPC) codes are proposed to compensate the rate loss of GLDPC codes. EXIT charts are used to analyze DGLDPC codes and EXIT functions for variable component codes are thoroughly discussed. Based on EXIT charts, differential evolution is used to optimize their threshold. Ensemble weight enumerators are generalized to protograph-based DGLDPC codes. Simulation results show that DGLDPC codes constructed based on these results can improve the performance of their LDPC and GLDPC counterparts in both the waterfall region and the error floor region.