LDPC codes which can correct three errors under iterative decoding

In this paper, we provide necessary and sufficient conditions for a column-weight-three LDPC code to correct all patterns up to three errors when decoded using Gallager A algorithm. We then provide a construction technique which results in a code satisfying the above conditions. We also provide numerical assessment of code performance via simulation results.

[1]  Shashi Kiran Chilappagari,et al.  Failures of the Gallager B Decoder: Analysis and Applications , 2006 .

[2]  Amin Shokrollahi,et al.  An Introduction to Low-Density Parity-Check Codes , 2000, Theoretical Aspects of Computer Science.

[3]  Bane V. Vasic,et al.  Diagnosis of weaknesses in modern error correction codes: a physics approach , 2005, Physical review letters.

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

[5]  Rüdiger L. Urbanke,et al.  The capacity of low-density parity-check codes under message-passing decoding , 2001, IEEE Trans. Inf. Theory.

[6]  David J. C. MacKay,et al.  Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check cCodes , 2003, MFCSIT.

[7]  Ali Emre Pusane,et al.  Pseudo-Codewords in LDPC Convolutional Codes , 2006, 2006 IEEE International Symposium on Information Theory.

[8]  Thomas J. Richardson,et al.  Error Floors of LDPC Codes , 2003 .

[9]  Emre Telatar,et al.  Finite-length analysis of low-density parity-check codes on the binary erasure channel , 2002, IEEE Trans. Inf. Theory.

[10]  Shashi Kiran Chilappagari,et al.  Error-Correction Capability of Column-Weight-Three LDPC Codes , 2007, IEEE Transactions on Information Theory.

[11]  P. Vontobel,et al.  Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes , 2005, ArXiv.

[12]  David Burshtein,et al.  Expander graph arguments for message-passing algorithms , 2001, IEEE Trans. Inf. Theory.

[13]  Shashi Kiran Chilappagari,et al.  Error Floors of LDPC Codes on the Binary Symmetric Channel , 2006, 2006 IEEE International Conference on Communications.

[14]  Evangelos Eleftheriou,et al.  Regular and irregular progressive edge-growth tanner graphs , 2005, IEEE Transactions on Information Theory.

[15]  Rüdiger L. Urbanke,et al.  Design of capacity-approaching irregular low-density parity-check codes , 2001, IEEE Trans. Inf. Theory.

[16]  David J. C. MacKay,et al.  Encyclopedia of Sparse Graph Codes , 1999 .

[17]  Roxana Smarandache,et al.  Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes , 2006, IEEE Transactions on Information Theory.