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Journal of Huaiyin Institute of Technology

A Grading Construction Method of Irregular LDPC Codes

Aimin Zhu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Low-Density Parity-Check codes have attracted great attention from academic world because of its excellent error-correcting performance.The main problem of its usage is the complexity of encoding.This paper proposes a method of construction of irregular Low-Density Parity-Check codes,which we call method of grading.Parity-Check matrix of the code constructed by this method not only has the characteristic of low-triangle which can lower the complexity of encoding but also has excellent performance that can match the constructed LDPC.

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Low-Density Parity-Check codes have attracted great attention from academic world because of its excellent error-correcting performance.The main problem of its usage is the complexity of encoding.This paper proposes a method of construction of irregular Low-Density Parity-Check codes,which we call method of grading.Parity-Check matrix of the code constructed by this method not only has the characteristic of low-triangle which can lower the complexity of encoding but also has excellent performance that can match the constructed LDPC.
The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.
In this paper, we propose an approach to construct a class of irregular low-density parity-check (LDPC) codes based on row partition.We divide the rows of LDPC check matrix into subsets and derive an approach to arrange '1' in each column to prevent low weight code words.When decoded by iterative algorithm, the proposed codes show performance with low error floor and are subject to few undetected errors.The LDPC codes constructed based on the proposed scheme have efficiently encoding structures.
To reduce the cycles in the Tanner graph which may affect the code performance,a recursive method to construct low-density parity-check(LDPC) codes was proposed.The method used a parity-check matrix of a short LDPC code as its mother matrix upon which a long code was constructed with circulant permutation matrices.By choosing the circulant permutation matrix parameters properly,the number of cycles having a given length in the Tanner graph of the constructed long codes were equal to or less than that of the short code.Either regular or irregular LDPC codes were constructed.Simulation results show that the LDPC codes constructed by this method have very low error-floor and almost no performance degradation due to their special structure as compared with random LDPC codes.
There is an important breakthrough in the field of forward error correction techniques, low-density parity-check (LDPC) codes. These codes have potential to approach the Shannon limit with reliable performance on a given channel, known as the channel capacity. Recently, researchers pay much more attention towards LDPC codes because its performance is better than Turbo codes. However, the LDPC code is the best when it is an irregular code and uses with a very large block-length. Although, the short block-length LDPC codes perform not so well, they are easy to implement in various practical applications. Therefore, there is still a demand of new development on the encoding side of LDPC codes for various ranges of code rate and code length so as to capable of using in many applications.This thesis proposes the development of quasi-cyclic (QC) LDPC codes for column weight 3. In the first part of this thesis, we propose a new construction algorithm of QC-LDPC codes for medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem (CRT). Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the maximum girth of the component codes. Simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods in terms of low error-floor, simple structure, high performance, and can reduce encoding complexity.In addition, this thesis also proposes two new construction methods for QC-LDPC codes, namely a base matrix method and a subtraction based method. A base matrix based method is a simple, less computational complexity method for constructing the exponent matrix (3, K) of girth 8, 10 and 12 of QC-LDPC codes. Another method is a subtraction method, which has a similar exponent matrix as a base matrix method and has a girth at least 8. Results indicate that the LDPC codes constructed from these two methods have flexibility for arbitrary block-column length K and have a similar BER performance if compared to existing methods.
In this paper, we present a method to design irregular structured low-density parity-check (LDPC) codes based on balanced incomplete block designs (BIBD). The problem of designing irregular structured LDPC codes that have good overall error performance for a wide range of code rates and block sizes with attractive storage requirements is attempted. The proposed codes are well structured and unlike random codes can lend themselves to a very low-complexity implementation. The codes constructed by this method have the girth at least 6 and they perform well with the sum-product iterative decoding algorithm. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance. The proposed LDPC codes demonstrate performance that is better than an average random LDPC code of similar block length, code rate and parity check matrix sparsity.