A lattice-based systematic recursive construction of quasi-cyclic LDPC codes

  • Authors:
  • M. Esmaeili;M. H. Tadayon

  • Affiliations:
  • Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran;Iran Telecommunication Research Center, Tehran, Iran

  • Venue:
  • IEEE Transactions on Communications
  • Year:
  • 2009

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Abstract

This paper presents a low-complexity recursive and systematic method to construct good well-structured low-density parity-check (LDPC) codes. The method is based on a recursive application of a partial Kronecker product operation on a given γ × q, q ≥ = 3 a prime, integer lattice L(γ × q). The (n - 1)- fold product of L(γ × q) by itself, denoted Ln(γ × q), represents a regular quasi-cyclic (QC) LDPC code, denoted Cγ × qn, of high rate and girth 6. The minimum distance of Cγ × qn is equal to that of the core code Cγ × q1 introduced by L(γ × q). The support of the minimum weight codewords in Cγ × qn are characterized by the support of the same type of codewords in Cγ × q1. From performance perspective the constructed codes compete with the pseudorandom LDPC codes.