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A matrix-theoretic approach for analyzing quasi-cyclic low-density parity-check codes

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4 Author(s)
Qiuju Diao ; Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA ; Qin Huang ; Shu Lin ; Abdel-Ghaffar, K.

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.

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Information Theory, IEEE Transactions on  (Volume:58 ,  Issue: 6 )