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International Symposium on Information Theory and its Applications

New constructions of variable-rate QC-LDPC codes by adding column-blocks or removing row-blocks

Chi‐Jen Wu, Chung-Hsuan Wang, Chi-chao Chao

Published Jan 1, 2016• 1 citation
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Abstract

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.

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•Jan 1, 2009•0 citations
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.
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.
In this paper, a new construction of quasi-cyclic low-density parity-check (QC-LDPC) codes for unequal error protection (UEP) is proposed. We first give a new class of UEP block codes. QC-LDPC codes with binomial-term parity-check matrices which can avoid girths less than 8 and achieve an enlarged upper bound on the minimum distance are also introduced. An effective UEP scheme based on the proposed UEP block codes and QC-LDPC codes which can provide flexible choice of protection levels is then presented. Simulation results show that the new QC-LDPC codes can achieve good performance and low error floors. The bits with different designed protection levels can indeed have unequal bit-error-rate performance.
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.
In this paper a new low complexity method for constructing binary quasi-cyclic low-density parity-check (QC-LDPC) codes is introduced. In the proposed method, each block-column of the parity check matrix H is made by a circulant matrix in a way that the associated Tanner graph is free of cycle four. Each circulant matrix in H is made by a generator column. The generator columns should be selected in a way that each associated circulant matrix and every two distinct circulant matrices are free of cycle four. The generator columns are made by row distance sets. An algorithm for generating distance sets and obtaining circulant matrices with columns of weight three is presented separately. Simplicity of construction and having a good flexible family of quasi cyclic LDPC codes both in rate and length are the main properties of the proposed method. The performance of the proposed codes is compared with that of the random-like and Array LDPC codes over an AWGN channel. Simulation results show that from the performance perspective, the constructed codes are competitive with random-like and Array LDPC codes.
This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of q X q square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (μ-flats) and points in Euclidean geometries, respectively. By decomposing the μ -flats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.