On the Construction of QC-LDPC Codes Based on Integer Sequence With Low Error Floor

Abstract

Quasi-cyclic low-density parity-check (QC-LDPC) codes have efficient hardware implementation and excellent correcting performance. However, the existence of trapping sets can affect the decoding performance. In this letter, a novel class of QC-LDPC codes based on integer sequence with column weight 3 and girth at least 8 is proposed. If the numbers in the sequence are different, the QC-LDPC codes free of elementary trapping sets ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${a}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b}$ </tex-math></inline-formula> ) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${a} \leq10$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${b} \leq $ </tex-math></inline-formula> 3 can be constructed. The row weight of the parity check matrix can be arbitrary and we give a lower bound of the circulant permutation matrix (CPM) size. Simulation results show that the generated codes have good performance with low error floor over AWGN channels.