Stopping set distribution of LDPC code ensembles
Orlitsky, A.
Viswanathan, K.
Zhang, J.
Dept. of Electr., Univ. of California, La Jolla, CA, USA;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: March 2005
Volume: 51,
Issue: 3
On page(s): 929-953
ISSN: 0018-9448
INSPEC Accession Number: 8327197
Digital Object Identifier: 10.1109/TIT.2004.842571
Current Version Published: 2005-02-28
Abstract
Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a √1-λ'(0)ρ'(1) fraction of codes with λ'(0)ρ'(1)<1, and in particular for almost all codes with smallest variable degree >2, the smallest nonempty stopping set is linear in the block length. Bounds on the average block error probability as a function of the erasure probability ε, showing in particular that for codes with lowest variable degree 2, if ε is below a certain threshold, the asymptotic average block error probability is 1-√1-λ'(0)ρ'(1)ε.
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