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Paper   IPM / M / 16480
School of Mathematics
  Title:   Anti quasi-cylic LDPC codes
  Author(s):  Mohammad Gholami (Joint with Z. Gholami)
  Status:   Published
  Journal: Journal de l'Ã?cole polytechnique â?? Mathématiques
  Vol.:  22
  Year:  2018
  Pages:   1116-1119
  Supported by:  IPM
LDPC codes based on affine permutation matrices, APM-LDPC codes, have been attracted recently, because of some advantages rather than QC-LDPC codes in minimum-distance, cycle distribution and error-rate performance. In this paper, circulant and anti-circulant permutation matrices are used to define a class of LDPC codes, called AQC-LDPC codes, which can be considered as an especial case of APM-LDPC codes. In fact, each AQC-LDPC code can be verified by a sign matrix and a slope matrix which are helpful to show each cycle in the Tanner graph by a modular linear equation. For the normal sign matrix A, if �??1 2 A, it is shown that the corresponding AQC-LDPC code has maximum-girth 8. Finally, two explicit constructions for AQC-LDPC codes with girths 6, 8 are presented which have some benefits rather than the explicitly constructed QC and APM LDPC codes in minimum-distance, cycle distributions and biterror-rate performances.

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