On the minimum pseudo-codewords of LDPC codes |
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Authors: | Shu-Tao Xia Fang-Wei Fu |
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Affiliation: | Graduate Sch., Tsinghua Univ., Shenzhen, China; |
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Abstract: | 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 minimum codewords. |
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