Integer Ring Sieve for Constructing Compact QC-LDPC Codes with Girths 8, 10, and 12

Alireza Tasdighi (1, 2) , E. Boutillon (1, 2)

1 UBS - Université de Bretagne Sud
2 Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance

This paper proposes a new method of constructing compact fully-connected Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with girth g = 8, 10, and 12. The originality of the proposed method is to impose constraints on the exponent matrix P to reduce the search space drastically. For a targeted lifting degree of N , the first step of the method is to sieve the integer ring ZN to make a particular subgroup with specific properties to construct the second column of P (the first column being filled with zeros). The remaining columns of P are determined recursively as multiples of the second column by adapting the sequentially multiplied column (SMC) method whereby a controlled greedy search is applied at each step. The codes constructed with the proposed semi-algebraic method show lengths that can be significantly shorter than their best counterparts in the literature.

Mots clés: QC-LDPC Code Construction; Girth; Multiplicative Group; Cyclic Subgroup; Greedy Search Method

Domaines: Electronique

Alireza Tasdighi, E. Boutillon. Integer Ring Sieve for Constructing Compact QC-LDPC Codes with Girths 8, 10, and 12. IEEE Transactions on Information Theory, 2022, 68 (1), pp.35-46. ⟨10.1109/TIT.2021.3116655⟩. ⟨hal-03375674⟩