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Expander graph arguments for message-passing algorithms

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2 Author(s)
Burshtein, D. ; Dept. of Electr. Eng.-Syst., Tel Aviv Univ., Israel ; Miller, G.

We show how expander-based arguments may be used to prove that message-passing algorithms can correct a linear number of erroneous messages. The implication of this result is that when the block length is sufficiently large, once a message-passing algorithm has corrected a sufficiently large fraction of the errors, it will eventually correct all errors. This result is then combined with known results on the ability of message-passing algorithms to reduce the number of errors to an arbitrarily small fraction for relatively high transmission rates. The results hold for various message-passing algorithms, including Gallager's hard-decision and soft-decision (with clipping) decoding algorithms. Our results assume low-density parity-check (LDPC) codes based on an irregular bipartite graph

Published in:

Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 2 )

Date of Publication:

Feb 2001

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