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IEEE International Symposium on Information Theory (ISIT)

Optimal Puncturing of Block-Type LDPC Codes and Their Fast Convergence Decoding

Song‐Nam Hong, Hyeong‐Gun Joo, Dong‐Joon Shin

Published Jul 1, 2006• 8 citations
Publisher

Abstract

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.

DOI
10.1109/isit.2006.261729

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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.
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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
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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.
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