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Journal of Chongqing University of Posts and Telecommunications

Design of rate-compatible QC-LDPC codes

Xia Wei

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Rate-compatible quasi-cyclic low-density parity-check(QC-LDPC)codes were designed with two construction methods.The first technique is based on code division,where a high-rate mother code is progressively divided into lower and lower rates;the other one adopts fractional row combination to yield a range of higher and higher rates form a relative low-rate mother code.The two methods cover different ranges of rates.Simulation result shows that the performance of these constructed rate-compatible QC-LDPC codes is as good as that of single rate codes which is straightly constructed based on the primitive elements of finite fields.

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arXiv:1211.3828•IEEE Transactions on Communications•Jul 16, 2013•33 citations
Rate-compatible quasi-cyclic low-density parity-check(QC-LDPC)codes were designed with two construction methods.The first technique is based on code division,where a high-rate mother code is progressively divided into lower and lower rates;the other one adopts fractional row combination to yield a range of higher and higher rates form a relative low-rate mother code.The two methods cover different ranges of rates.Simulation result shows that the performance of these constructed rate-compatible QC-LDPC codes is as good as that of single rate codes which is straightly constructed based on the primitive elements of finite fields.
This paper proposes a new technique for constructing the Quasi-Cyclic low density parity check (QC-LDPC) codes based on row division method. The new codes offer more flexibility in term of girth, code rates and codeword length. In this method of code construction, the rows are used to form as the distance graph. Then they are transformed to a parity-check matrix in order to acquire the desired girth. The new QC-LDPC codes show good bit-error rate performance as compared to the renowned Mackay codes for given values of Eb/Noby 0.12 dB at BER of10-7.
A class of rate-compatible (RC) quasi-cycle low-density parity-check (QC-LDPC) codes that have linear encodable complexity and low error floor is presented. To ensure linear encoding complexity, a lower triangular (LT) form for the parity part of the mother parity-check matrix is designed. By the designed LT form, a recursive encoding strategy is proposed. This encoding strategy can achieve linear encodable complexity, which is completely proportional to the code length. To guarantee good performances for a wide range of code rates, a layered short-cycle optimization algorithm is designed to obtain good girth distribution, and a layered density evolution algorithm is used to optimize degree distributions of each code rate. Then, a class of RC QC-LDPC codes can be obtained by both extension and puncturing from the optimized QC-LDPC mother code with rate 1/2. Simulation results show that no error floor is exhibited for the proposed RC QC-LDPC codes at FER=10-5. The practical performance at BER=10-6shows a gap of about 1.477 dB to the Shannon limit.
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.
In this paper, new constructions of variable-rate quasi-cyclic low-density parity-check (QC-LDPC) codes are proposed. The criteria which guarantee that a higher-rate QC-LDPC code can be obtained by adding column-blocks to or removing row-blocks from the parity-check matrix of a given lower-rate QC-LDPC code are derived. Based on these criteria, new families of variable-rate QC-LDPC codes can be constructed. Simulation results show that the constructed codes provide a variety of error-protection capabilities against different channel conditions.
In this paper, a scheme to construct the high-rate regular quasi-cyclic low-density parity-check (QC-LDPC) codes is developed based on the finite geometry low-density parity-check (LDPC) codes. To achieve this, we first decompose the EG-LDPC code into a set of the block submatrices with each of them being cyclic. Utilizing the decomposed structure, we then construct an auxiliary matrix to facilitate us for identifying and eliminating 6-cycles of the block submatrices. In the simulation, seven regular QC-LDPC codes with code rates being 4/5, 7/8, 10/11, 11/12, and 12/13 of moderate code lengths are constructed with this scheme. The performances of these codes demonstrate the effectiveness of the proposed scheme.
For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.