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IEEE International Symposium on Signal Processing and Information Technology (ISSPIT)

Constructing Quasi-Cyclic LDPC codes Using a Search Algorithm

Gabofetswe Malema

Published Dec 1, 2007• 3 citations
Publisher

Abstract

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.

DOI
10.1109/isspit.2007.4458089

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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.
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