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EURASIP Journal on Advances in Signal Processing

Quasi-Cyclic LDPC Codes of Column-Weight Two Using a Search Algorithm

Gabofetswe Malema, Michael John Liebelt

Published Apr 19, 2007• 12 citations
Publisher

Abstract

This article introduces a search algorithm for constructing quasi-cyclic LDPC codes of column-weight two. To obtain a submatrix structure, rows are divided into groups of equal sizes. Rows in a group are connected in their numerical order to obtain a cyclic structure. Two rows forming a column must be at a specified distance from each other to obtain a given girth. The search for rows satisfying the distance is done sequentially or randomly. Using the proposed algorithm regular and irregular column-weight-two codes are obtained over a wide range of girths, rates, and lengths. The algorithm, which has a complexity linear with respect to the number of rows, provides an easy and fast way to construct quasi-cyclic LDPC codes. Constructed codes show good bit-error rate performance with randomly shifted codes performing better than sequentially shifted ones.

DOI
10.1155/2007/45768

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This article introduces a search algorithm for constructing quasi-cyclic LDPC codes of column-weight two. To obtain a submatrix structure, rows are divided into groups of equal sizes. Rows in a group are connected in their numerical order to obtain a cyclic structure. Two rows forming a column must be at a specified distance from each other to obtain a given girth. The search for rows satisfying the distance is done sequentially or randomly. Using the proposed algorithm regular and irregular column-weight-two codes are obtained over a wide range of girths, rates, and lengths. The algorithm, which has a complexity linear with respect to the number of rows, provides an easy and fast way to construct quasi-cyclic LDPC codes. Constructed codes show good bit-error rate performance with randomly shifted codes performing better than sequentially shifted ones.
This article presents a search algorithm for constructing regular and irregular quasi-cyclic LDPC codes. Code rows and columns are divided into j (column weight) and k (row-weight) or more groups respectively. Rows or columns in a group are connected to the same group and in order of appearance. Grouping of rows and columns forms sub-matrices. The sequential row-column connections order creates a cyclic structure in sub-matrices. The row-column constraint is observed to avoid four-cycles. The proposed algorithm is flexible compared to other methods. It obtains codes over a wide range of girths, rates and lengths. Bit-error rate simulations show that obtained codes have good performance with randomly searched codes performing better that sequentially searched codes.
In this paper a modified bit-filling algorithm is used for constructing column-weight two quasi-cyclic low-density parity-check codes with large girths. Code rows are divided into groups. A column is connected to two rows from different groups, which are apart by at least a specified minimum length. Rows that meet the minimum length are searched sequentially. Group rows are connected to consecutive columns resulting in a cyclic structure in the code matrix. Larger codes can be obtained by using larger row groups. Compared to other methods, the algorithm provides an easy and fast way to construct codes of a wide range of rates, girths and lengths. Constructed codes show good bit error rate performance. They are also easily implementable in hardware compared to those obtained using the original bit filling algorithm
This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.
Thisarticle presents asearch algorithm forcon-proposed algorithm withsomeobtained codessizes, girths structing regular andirregular quasi-cyclic LDPCcodes. Code andrates. Section IIIevaluates bit-error rateperformances rowsandcolumns aredivided intoj (column weight) andk (row-weight) ormoregroupsrespectively. Rowsorcolumns in a groupareconnected tothesamegroupandinorderof Section IV. appearance. Grouping ofrowsandcolumns forms sub-matrices.II. PROPOSEDQC-LDPCSEARCHALGORITHM Thesequential row-column connections ordercreates a cyclic structure insub-matrices. Therow-column constraint isobservedIn(8)quasi-cyclic column-weight twocodesareconstructed toavoid four-cycles. Theproposed algorithm isflexible comparedbasedonadistance graph representation. A desired girth g,is toother methods. Itobtains codes overawiderangeofgirths, obtained bysearching andconnecting tworowsthatareata rates andlengths. Bit-error ratesimulations showthatobtained codeshavegoodperformance withrandomly searched codesdistance ofatleastg Weextend thesearch algorithmiproposed performing better thatsequentially searched codes. in(8)toconstruct QC-LDPCwithcolumn-weights higher than two.LDPCcoderowsandcolumns aredivided intogroups
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.
In order to find a kind of linear code with simple structure and approaching Shannon limit,based on the algorithm of constructing quasi-cyclic low density parity check(LDPC) codes and combined with the characteristic of low density lattice codes(LDLC),the LDLC with girth-8 through improving the algorithm was constructed.The new algorithm ensures the LDLC generating sequence distribute in each row or each column randomly and its uniformity in each row and each column.Meanwhile this article analyses the complexity of the algorithm.Simulation result in AWGN channel shows that the performance of girth-8 LDLC code using the proposed algorithm is better than the present girth-6 LDLC code.