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International Journal of Engineering & Technology

Construction and performance analysis of diagonally shifted column structured RPM based regular quasi cyclic-LDPC codes with girth 10

Jitendra Pratap Singh Mathur, Alpana Pandey

Published Oct 14, 2018• 0 citations
Publisher

Abstract

In this manuscript, QC-LDPC (Quasi Cyclic Low-Density Parity Check Codes) are constructed by the diagonally Shifted Column structured Random Permutation Method (RPM) with girth 10. In this proposed method, Random Permutation based Parity Check Matrix, Base Matrix and Zero Matrices has been constructed with a column structured approach using Lower Upper decomposition technique. The row-column mapping Technique is applied to create the sparse behavior of Regular RPM based Quasi Cyclic LDPC Codes. The construction of code is obtainable by means of column weight three and row weight six. Those codes are decoded with Log Domain Sum Product Algorithm. The constructed Sparse Regular RPM-QC-LDPC Codes have low error performance and compared with other existing results.

DOI
10.14419/ijet.v7i4.18644

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In this manuscript, QC-LDPC (Quasi Cyclic Low-Density Parity Check Codes) are constructed by the diagonally Shifted Column structured Random Permutation Method (RPM) with girth 10. In this proposed method, Random Permutation based Parity Check Matrix, Base Matrix and Zero Matrices has been constructed with a column structured approach using Lower Upper decomposition technique. The row-column mapping Technique is applied to create the sparse behavior of Regular RPM based Quasi Cyclic LDPC Codes. The construction of code is obtainable by means of column weight three and row weight six. Those codes are decoded with Log Domain Sum Product Algorithm. The constructed Sparse Regular RPM-QC-LDPC Codes have low error performance and compared with other existing results.
This paper presents Bit error Rate performance Analysis of Quasi Cyclic Low Density Parity Check Codes (QC-LDPC) with girth 6 using Log Domain sum product and Simple Log Domain Sum Product Algorithm for Decoding. The approach to construct Parity Check matrix for LDPC codes is based on sparse Lower Upper decomposition. Then to create QC-LDPC matrix counter shifting, interleave mapping, Set XORing, Circulant Shifting and Randomization processes are being used. The constructed QC-LDPC codes is of a girth 6 on / code Rate have row weight 6 and column weight 3. Bit error rate performance is done through simulation to be calculated for various code length such as code I (960, 480), code II (1980, 990) and code III (1080, 540).
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
A new approach is proposed for constructing regular low-density parity-check (LDPC) codes based on tensor product of matrices. In this paper, first a general construction method of regular LDPC codes exploiting permutation matrices is described. Constructed codes have a quasi-cyclic structure with no short cycles of length 4 in their Tanner graph, hence simple encoding while maintaining good performance is achieved. The paper also demonstrates a generalized design, which covers a large family of LDPC codes and number of other construction methods. The new generalized LDPC codes are defined by a small number of parameters and cover a large set of code lengths and rates. Using these codes, LDPC matrices of any column weight and row weight can be constructed. Performance of these codes under iterative decoding compares well with other well-structured as well as random LDPC codes
Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an orthogonal structure suitable for quantum error correction. By utilizing algebraic techniques, short cycles are eliminated, which improves error correction performance. Additionally, this method is extended to non-binary LDPC codes and spatially-coupled LDPC codes, demonstrating that both the girth and orthogonality can be preserved. The results of this study enable the design of high-performance quantum error-correcting codes without the need for random search.