On the Expanding Properties of Gallager's LDPC Matrices

This paper investigates expanding properties of ensembles of random bipartite graphs whose adjacency matrices are Gallager's low-density parity-check matrices. Two methods for calculating the expansion coefficient are demonstrated. It is shown that in the ensemble of the considered bipartite graphs, there exist graphs which have better expanding properties than the previously known expanders.

[1]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[2]  Robert Michael Tanner,et al.  A recursive approach to low complexity codes , 1981, IEEE Trans. Inf. Theory.

[3]  D. Spielman,et al.  Expander codes , 1996 .

[4]  J. Boutros,et al.  Generalized low density (Tanner) codes , 1999, 1999 IEEE International Conference on Communications (Cat. No. 99CH36311).

[5]  Gilles Zémor,et al.  On expander codes , 2001, IEEE Trans. Inf. Theory.

[6]  Shlomo Hoory,et al.  On codes from hypergraphs , 2004, Eur. J. Comb..

[7]  Rolf Johannesson,et al.  Asymptotically Good Woven Codes with Fixed Constituent Convolutional Codes , 2007, 2007 IEEE International Symposium on Information Theory.

[8]  M. Loncar,et al.  On the asymptotic performance of low-complexity decoded LDPC codes with constituent hamming codes , 2008, 2008 5th International Symposium on Turbo Codes and Related Topics.

[9]  Rolf Johannesson,et al.  Woven graph codes over hypergraphs , 2008 .

[10]  Rolf Johannesson,et al.  On the erasure-correcting capabilities of low-complexity decoded LDPC codes with constituent Hamming codes , 2008 .