The design of structured regular LDPC codes with large girth

The paper introduces three new classes of structured regular (n, 2, k) LDPC codes with girth 12, 16, and 20, respectively. These codes are systematically constructed, well structured, and have uniform row and column weights, which make them able to simplify greatly the implementation of LDPC coders. Their large girth improves their decoding performance. Simulation results compare their bit error rate (BER) performance over additive white Gaussian noise (AWGN) channels with randomly constructed LDPC codes. When concatenated with error-correcting codes such as Reed-Solomon codes, LDPC codes with j=2 are promising for data storage and other applications.

[1]  Jose M. F. Moura,et al.  Large-girth LDPC codes based on graphical models , 2003, 2003 4th IEEE Workshop on Signal Processing Advances in Wireless Communications - SPAWC 2003 (IEEE Cat. No.03EX689).

[2]  Sarah J. Johnson,et al.  Regular low-density parity-check codes from combinatorial designs , 2001, Proceedings 2001 IEEE Information Theory Workshop (Cat. No.01EX494).

[3]  X. Jin.  Factor graphs and the Sum-Product Algorithm , 2002 .

[4]  D.J.C. MacKay,et al.  Good error-correcting codes based on very sparse matrices , 1997, Proceedings of IEEE International Symposium on Information Theory.

[5]  Shu Lin,et al.  Low-density parity-check codes based on finite geometries: A rediscovery and new results , 2001, IEEE Trans. Inf. Theory.

[6]  Bane V. Vasic,et al.  Structured iteratively decodable codes based on Steiner systems and their application in magnetic recording , 2001, GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270).

[7]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[8]  B. V. K. Vijaya Kumar,et al.  Low complexity LDPC codes for partial response channels , 2002, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE.

[9]  Michael Horstein,et al.  Review of 'Low-Density Parity-Check Codes' (Gallager, R. G.; 1963) , 1964, IEEE Transactions on Information Theory.

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

[11]  David J. C. MacKay,et al.  Good Codes Based on Very Sparse Matrices , 1995, IMACC.