Computer Science – Information Theory
Scientific paper
2008-08-26
Advances in Mathematics of Communications (AMC), Vol. 2, No 4, (2008) pp. 433 - 450.
Computer Science
Information Theory
16 pages
Scientific paper
10.3934/amc.2008.2.433
Codes on hypergraphs are an extension of the well-studied family of codes on bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes on regular t-partite hypergraphs whose minimum distance improves earlier estimates of the distance of bipartite-graph codes. They also suggested a decoding algorithm for such codes and estimated its error-correcting capability. In this paper we study two aspects of hypergraph codes. First, we compute the weight enumerators of several ensembles of such codes, establishing conditions under which they attain the Gilbert-Varshamov bound and deriving estimates of their distance. In particular, we show that this bound is attained by codes constructed on a fixed bipartite graph with a large spectral gap. We also suggest a new decoding algorithm of hypergraph codes that corrects a constant fraction of errors, improving upon the algorithm of Bilu and Hoory.
Barg Alexander
Mazumdar Arya
Zemor Gilles
No associations
LandOfFree
Codes on hypergraphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Codes on hypergraphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Codes on hypergraphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-281228