On the minimum pseudo-codewords of LDPC codes

@article{Xia2006OnTM,
  title={On the minimum pseudo-codewords of LDPC codes},
  author={Shu-Tao Xia and Fang-Wei Fu},
  journal={IEEE Communications Letters},
  year={2006},
  volume={10},
  pages={363-365}
}
In this letter, we study the minimum pseudo-codewords of low-density parity-check (LDPC) codes under linear programming (LP) decoding. We show that a lower bound of Chaichanavong and Siegel on the pseudo-weight of a pseudo-codeword is tight if and only if this pseudo-codeword is a real multiple of a codeword. Using this result we further show that for some LDPC codes, e.g., Euclidean plane and projective plane LDPC codes, there are no other minimum pseudo-codewords except the real multiples of… CONTINUE READING
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