A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes

Details A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes

2007-02-25

arxiv.org/abs/cs/0702146v1

Computer Science

Information Theory

Comments, submitted to IEEE Transactions on Information Theory

Scientific paper

We address the problem,`Is a local tree structure sufficient for the local optimality of message passing algorithm in low density parity check codes?'.It is shown that the answer is negative. Using this observation, we pinpoint a flaw in the proof of Theorem 1 in the paper `The Capacity of Low-Density Parity-Check Codes Under Message-Passing Decoding' by Thomas J. Richardson and R\"udiger L.Urbanke\cite{RUCapacity}. We further provide a new proof of that theorem based on a different argument.

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