An introduction to low-density parity-check codes
Theoretical aspects of computer science
IEEE Transactions on Information Theory - Part 1
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Expander graph arguments for message-passing algorithms
IEEE Transactions on Information Theory
Using linear programming to Decode Binary linear codes
IEEE Transactions on Information Theory
LP Decoding Corrects a Constant Fraction of Errors
IEEE Transactions on Information Theory
Instanton-based techniques for analysis and reduction of error floors of LDPC codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Two-bit message passing decoders for LDPC codes over the binary symmetric channel
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
On trapping sets and guaranteed error correction capability of LDPC codes and GLDPC codes
IEEE Transactions on Information Theory
Error correction capability of column-weight-three LDPC codes under the Gallager A algorithm-Part II
IEEE Transactions on Information Theory
An Information Theoretic Approach to Constructing Robust Boolean Gene Regulatory Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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In this paper, the error-correction capability of column-weight-three low-density parity-check (LDPC) codes when decoded using the Gallager A algorithm is investigated. It is proved that a necessary condition for a code to correct all error patterns with up to k ≥ 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, it is shown that given any α 0, ∃ N such that ∀ n N, no code in the ensemble of column-weight-three codes can correct all αn or fewer errors. The results are extended to the bit flipping algorithms.