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International Conference on Inventive Computing and Informatics (ICICI)

Performance analysis of QC-LDPC codes with girth 6 using Log Domain sum product algorithm

Jitendra Pratap Singh Mathur, Alpana Pandey

Published Nov 1, 2017• 0 citations
Publisher

Abstract

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).

DOI
10.1109/icici.2017.8365366

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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).
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.
Quasi Cyclic Low Density Parity Check(QC-LDPC) code is an important branch of LDPC code research.It is a kind of constructed LDPC code with check matrix H constructed by quasi cyclic method.IEEE 802.16e proposes a parity check matrix with quasi cyclic character which makes the encoding and hardware easy to be implemented.This article will mainly introduce the encoding process and analyze the decoding performance of various decoding algorithms.Simulations show that Min-Sum(MS) algorithm compares to the Log-BP performance has approximately 0.5dB loss for high-speed rate coding.And the performance of Normalized Min-Sum(NMS) and Row Weight Matched Min-Sum(Rwm-MS) with relatively low complexity is nearly the same as that of Log-BP algorithm.
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.
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.
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.
The essential conditions for quasi-cyclic low-density parity-check codes(QC-LDPC codes) to have no Girth 4 are given.This solves the problem of designing without-girth-4 QC-LDPC codes of any length.Adjusting the dimension and shift factors of the circulant sub-matrices of the given sparse parity-check matrices according to the proposed theorems,the QC-LDPC codes without girth 4 are constructed.The matrice equation set for girth 4 check is established.Through setting the dimension and shift factors of the circulant sub-matrices,we can check whether the QC-LDPC codes have Girth 4 or not.We can multiply the dimension of the circulant sub-matrices to get the QC-LDPC codes without Girth 4 of different lengths.Our theorems keep the QC-LDPC codes without Girth 4 along with increasing of the code length.Compared to the previous algorithms,the proposed test algorithm decreases computation,shortens the test time and reduces the complexity of structuring the parity-check matrix.Experimental results indicate that the designed QC-LDPC codes achieve good bit error rate(BER) performance.