Construction of full rank parity check matrix and systematic encoding for nonbinary quasi-cyclic LDPC codes

Hengzhou Xu, Huaan Li, Min Zhu +2 more

Po‐Chun Yang, Chung-Hsuan Wang, Chi-Chao Chao

Quasi-cyclic low-density parity-check (QC-LDPC) codes are an important class of LDPC codes which can be encoded and decoded with low complexity and suitable for many applications. As the code dimension, which describes the number of protected information bits, is equal to the code length minus the rank of the parity-check matrix and the parity-check matrix for QC-LDPC codes is usually not full-rank, determining the rank of the parity-check matrix is of essential importance. In this paper, we study the rank of the parity-check matrix for QC-LDPC codes based on the associated polynomials for circulant matrices. A formula for the rank of the parity-check matrix with only one row-block is first derived. We then extend the result to matrices with two, three, or more row-blocks. Some bounds are also presented for matrices with arbitrary numbers of row-blocks. Furthermore, the exact rank is determined for a class of algebraically constructed parity-check matrices.

学 萩原, Manabu Hagiwara, Kenta Kasai +3 more

Xinmei Wang

In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.

Chien-Fu Tseng, Jenn‐Hwan Tarng

In this letter, we present a low-complexity encoding method for quasi-cyclic (QC) low-density parity-check (LDPC) codes in the case of non-full-rank parity-check matrices. Gaussian elimination can achieve systematic encoding, but it is usually too complex to implement. For QC-LDPC codes, efficient encoding methods have been presented by using shift-registers, but the encoded codewords are not systematic when parity-check matrices are non-full-rank. However, a systematic structure is important in practice. Therefore, we propose an encoding method which allows all information bits appear piecewise in the codeword, called piecewise systematic encoding.

Yu Yi, Hye Kyung Jang, Moon Ho Lee +1 more