A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes
<|reference_start|>A Local Tree Structure is NOT Sufficient for the Local Optimality of Message-Passing Decoding in Low Density Parity Check Codes: 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.<|reference_end|>
@article{xu2007a,
    title={A Local Tree Structure is NOT Sufficient for the Local Optimality of
  Message-Passing Decoding in Low Density Parity Check Codes},
    author={Weiyu Xu},
    journal={arXiv preprint arXiv:cs/0702146},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0702146},
    primaryClass={cs.IT math.IT}
}