Locally Testable Codes Require Redundant Testers
SIAM Journal on Computing
Bounds on the minimum code distance for nonbinary codes based on bipartite graphs
Problems of Information Transmission
Hi-index | 754.84 |
New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. The bounds apply to regular LDPC codes, and sometimes also to right-regular LDPC codes. Their derivation is based on combinatorial arguments and linear programming. The new bounds improve upon the previous bounds due to Burshtein et al. It is proved that at least for high rates, regular LDPC codes with full-rank parity-check matrices have worse relative minimum distance than the one guaranteed by the Gilbert-Varshamov bound.