DocumentCode :
1167200
Title :
Which Codes Have 
-Cycle-Free Tanner Graphs?
-Cycle-Free Tanner Graphs?Author :
Halford, Thomas R. ; Grant, Alex J. ; Chugg, Keith M.
Author_Institution :
Commun. Sci. Inst., Univ. of Southern California, Los Angeles, CA
Volume :
52
Issue :
9
fYear :
2006
Firstpage :
4219
Lastpage :
4223
Abstract :
Let C be an [n,k,d] binary linear code with rate R=k/n and dual C perp. In this correspondence, it is shown that C can be represented by a 4-cycle-free Tanner graph only if: pdperples lfloorradicnp(p-1)+n2/4+n/2 rfloorwhere p=n-k and dperp is the minimum distance of C perp. By applying this result, it is shown that 4-cycle- free Tanner graphs do not exist for many classical binary linear block codes
Keywords :
binary codes; block codes; cyclic codes; graph theory; linear codes; 4-cycle-free Tanner graph; binary linear block code; Australia; Bipartite graph; Block codes; Graph theory; Graphical models; Information theory; Iterative algorithms; Iterative decoding; Lakes; Parity check codes; Cycles; Tanner graphs; girth; graphical models of codes; iterative decoding;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2006.880060
Filename :
1683938
Link To Document :
