Upper bound on the minimum distance of LDPC codes over GF(q) based on counting the number of syndromes

Abstract

In [1] a syndrome counting based upper bound on the minimum distance of regular binary LDPC codes is given. In this paper we extend the bound to the case of irregular and generalized LDPC codes over GF(q). A comparison with the lower bound for LDPC codes over GF(q), upper bound for the codes over GF(q), and the shortening upper bound for LDPC codes is made. The new bound is shown to lie under the Gilbert–Varshamov bound at high rates.

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Correspondence to A. A. Frolov.

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Original Russian Text © A.A. Frolov, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 1, pp. 8–15.

The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

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Frolov, A.A. Upper bound on the minimum distance of LDPC codes over GF(q) based on counting the number of syndromes. Probl Inf Transm 52, 6–13 (2016). https://doi.org/10.1134/S0032946016010026

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Keywords

  • Information Transmission
  • LDPC Code
  • Check Node
  • Weight Enumerator
  • Tanner Graph