ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
On the design and alphabet size of Roth-Skachek nearly MDS expander codes
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On LP decoding of nonbinary expander codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
The minimum distance of graph codes
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Linear time decoding of regular expander codes
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Bounds on the minimum code distance for nonbinary codes based on bipartite graphs
Problems of Information Transmission
Linear-time decoding of regular expander codes
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
| Hi-index | 754.84 |
A construction of expander codes is presented with the following three properties: i) the codes lie close to the Singleton bound, ii) they can be encoded in time complexity that is linear in their code length, and iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can replace maximum-distance separable (MDS) outer codes in concatenated constructions, thus resulting in linear-time encodable and decodable codes that approach the Zyablov bound or the capacity of memoryless channels. The presented construction improves on an earlier result by Guruswami and Indyk in that any rate and relative minimum distance that lies below the Singleton bound is attainable for a significantly smaller alphabet size