Geometry based designs of LDPC codes

In this paper we construct three types of low-density parity-check codes with column weight j = 3 based on geometries in graphical models. Low-density parity-check codes with j > 2 are desired because their minimum distance improves linearly with the code block length n. The codes we present here have girth 8 and girth 10. All codes are regular and well-structured. These codes have flexible block lengths and code rates, and may be used in the area of communications and data storage. Our simulation results show that they have better bit-error-rate decoding performance and lower error floors in additive white Gaussian noise channels than randomly constructed low-density parity-check codes.

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

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

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

[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]  Jung-Fu Cheng,et al.  Turbo Decoding as an Instance of Pearl's "Belief Propagation" Algorithm , 1998, IEEE J. Sel. Areas Commun..

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

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

[8]  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).

[9]  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).

[10]  José M. F. Moura,et al.  The design of structured regular LDPC codes with large girth , 2003, GLOBECOM '03. IEEE Global Telecommunications Conference (IEEE Cat. No.03CH37489).

[11]  J. Moura,et al.  Structured low-density parity-check codes , 2004, IEEE Signal Processing Magazine.

[12]  Urs Niesen,et al.  A class of structured LDPC codes with large girth , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).