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On algebraic construction of Gallager and circulant low-density parity-check codes

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5 Author(s)
Tang, H. ; PMC-Sierra Inc., Portland, OR, USA ; Jun Xu ; Yu Kou ; Shu Lin
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This correspondence presents three algebraic methods for constructing low-density parity-check (LDPC) codes. These methods are based on the structural properties of finite geometries. The first method gives a class of Gallager codes and a class of complementary Gallager codes. The second method results in two classes of circulant-LDPC codes, one in cyclic form and the other in quasi-cyclic form. The third method is a two-step hybrid method. Codes in these classes have a wide range of rates and minimum distances, and they perform well with iterative decoding.

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Information Theory, IEEE Transactions on  (Volume:50 ,  Issue: 6 )