A Matrix-Theoretic Approach for Analyzing Quasi-Cyclic Low-Density Parity-Check Codes

作者：Diao Qiuju^*; Huang Qin; Lin Shu; Abdel Ghaffar Khaled

来源：IEEE Transactions on Information Theory, 2012, 58(6): 4030-4048.

DOI：10.1109/TIT.2012.2184834

• Array of circulants
• code construction
• Fourier transform
• low-density parity-check (LDPC) code
• quasi-cyclic (QC) code
• rank

A matrix-theoretic approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is developed. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is amicable to the analysis and construction of quasi-cyclic low-density parity-check codes since it takes into account the specific parity-check matrix used for decoding with iterative message-passing algorithms. Based on this approach, the dimension of the codes and parity-check matrices for the dual codes can be determined. Several algebraic and geometric constructions of quasi-cyclic codes are presented as applications along with simulation results showing their performance over additive white Gaussian noise channels decoded with iterative message-passing algorithms.

• 出版日期2012-6
• 单位北京航空航天大学