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Which Codes Have 4 -Cycle-Free Tanner Graphs?

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3 Author(s)
Halford, T.R. ; Commun. Sci. Inst., Univ. of Southern California, Los Angeles, CA ; Grant, A.J. ; Chugg, K.M.

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

Published in:

Information Theory, IEEE Transactions on  (Volume:52 ,  Issue: 9 )

Date of Publication:

Sept. 2006

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