SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
Error-correction capability of column-weight-three LDPC codes
IEEE Transactions on Information Theory
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
Iterative approximate linear programming decoding of LDPC codes with linear complexity
IEEE Transactions on Information Theory
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
Monotone circuits for the majority function
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
| Hi-index | 755.08 |
We show how expander-based arguments may be used to prove that message-passing algorithms can correct a linear number of erroneous messages. The implication of this result is that when the block length is sufficiently large, once a message-passing algorithm has corrected a sufficiently large fraction of the errors, it will eventually correct all errors. This result is then combined with known results on the ability of message-passing algorithms to reduce the number of errors to an arbitrarily small fraction for relatively high transmission rates. The results hold for various message-passing algorithms, including Gallager's hard-decision and soft-decision (with clipping) decoding algorithms. Our results assume low-density parity-check (LDPC) codes based on an irregular bipartite graph