• Title/Summary/Keyword: Gilbert-Varshamov bound

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A Weight on Boolean Algebras for Cryptography and Error Correcting Codes (암호학 및 오류 수정 코드를 위한 부울 대수 가중치 연구)

  • Yon, Yong-Ho;Kang, An-Na
    • Journal of Advanced Navigation Technology
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    • v.15 no.5
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    • pp.781-788
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    • 2011
  • A sphere-packing problem is to find an arrangement of the spheres to fill as large area of the given space as possible, and covering problems are optimization problems which are dual problems to the packing problems. We generalize the concepts of the weight and the Hamming distance for a binary code to those of Boolean algebra. In this paper, we define a weight and a distance on a Boolean algebra and research some properties of the weight and the distance. Also, we prove the notions of the sphere-packing bound and the Gilbert-Varshamov bound on Boolean algebra.

Improved Upper Bounds on Low Density Parity Check Codes Performance for the Input Binary AWGN Channel

  • Yu Yi;Lee, Moon-Ho
    • Proceedings of the IEEK Conference
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    • 2002.06a
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    • pp.323-326
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    • 2002
  • In this paper, we study the improved bounds on the performance of low-density parity-check (LDPC) codes over binary-input additive white Gaussian noise (AWGN) channels with belief propagation (BP) decoding in log domain. We define an extended Gallager ensemble based on a new method of constructing parity check matrix and make use of this way to improve upper bound of LDPC codes. At the same time, many simulation results are presented in this paper. These results indicate the extended Gallager ensembles based on Hamming codes have typical minimum distance ratio, which is very close to the asymptotic Gilbert Varshamov bound and the superior performance which is better than the original Gallager ensembles.

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