Extremal graphs without three-cycles or four-cycles
Journal of Graph Theory
Spectral Techniques in Graph Algorithms
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Extremal Graph Theory
Error-correction capability of column-weight-three LDPC codes
IEEE Transactions on Information Theory
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
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Error exponents of expander codes
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
On the Error Correction of Regular LDPC Codes Using the Flipping Algorithm
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
Hi-index | 754.90 |
The relation between the girth and the guaranteed error correction capability of γ-left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3gamma;/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed error correction capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed error correction capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.