Details

Autor(en) / Beteiligte

• Tasdighi, Alireza
• Boutillon, Emmanuel

Titel

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

Ist Teil von

• IEEE transactions on information theory, 2022-01, Vol.68 (1), p.35-46

Ort / Verlag

IEEE

Erscheinungsjahr

2022

Link zum Volltext

• IEEE_Xplore

Quelle

IEEE Xplore Digital Library

Beschreibungen/Notizen

• This paper proposes a new method of constructing compact fully-connected Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with girth <inline-formula> <tex-math notation="LaTeX">g </tex-math></inline-formula> = 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 <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>, the first step of the method is to sieve the integer ring <inline-formula> <tex-math notation="LaTeX">\mathbb {Z}_{N} </tex-math></inline-formula> to make a particular sub-group 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.