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IEEE Vehicular Technology Conference

Fast convergence algorithm for LDPC Codes

Frank Kienle, Timo Lehnigk-Emden, Norbert Wehn

Published Sep 8, 2006• 10 citations
Publisher

Abstract

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

DOI
10.1109/vetecs.2006.1683286

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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
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.
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
As for the sum-product decoding algorithm of low density parity check(LDPC) codes,a difference-based decoding method is proposed.The main idea is shown as follows: the messages passed on the bipartite graph of LDPC are based on the probability differences,and the updates of both check nodes and message nodes are carried out on some special addition domain.As for the update of check nodes,only some lowest differences can be selected for reducing computational complexity.In contrast with the traditional log-likelyhood-ratio-based(LLR-based) decoding method,the proposed method has much lower complexity,while it has no obvious loss of performance and convergence.
In this paper, we study and propose a puncturing algorithm of block-type low-density parity-check (B-LDPC) codes. This optimal puncturing algorithm is derived from the fact that puncturing of parity bits is equivalent to merging the check nodes. Furthermore, we propose a new decoding algorithm suitable for the punctured B-LDPC codes. This decoding algorithm needs not only smaller number of operations at each iteration, but also shows faster decoding convergence speed than the conventional erasure decoding algorithm. If the optimally punctured B-LDPC code is decoded by the new decoding algorithm, it results in the same performance as the unpunctured B-LDPC code of the same code rate.
Low density parity check (LDPC) codes are amongst the most powerful codes known today. They are decoded iteratively by a message-passing algorithm. For this, an inherent stopping criterion exists for decodable blocks based on parity checks. For undecodable blocks, typically, a fixed number of iterations are carried out before the decoding procedure is terminated, which is a waste of energy and time. We present a stopping criterion which detects undecodable blocks in an early stage of the decoding process. The novel stopping criterion works for floating and fixed point implementations. It greatly reduces the average number of required iterations without any loss in communication performance.
An adaptive decoding scheme for low-density parity-check (LDPC) codes is proposed for accelerating the convergence of message-passing algorithms. The evolution of adaptive weighting factor with the number of decoding iterations and stopping criterion are based on the cross-entropy between two consecutive a posteriori probabilities distribution of the soft output of decoder. Information-theoretic support and extensive simulations are provided to demonstrate the efficiency of the proposed algorithm for LDPC decoding. The proposed adaptive decoding algorithm can reduce significantly the average number of iterations of decoder while having a comparable or even better performance than conventional message-passing algorithms.