Abstract
In this paper, we study a class of nonbinary LDPC (NBLDPC) codes whose parity-check matrices have column weight 2, called NBLDPC cycle codes. We propose a design framework of 2 , ρ -regular binary quasi-cyclic (QC) LDPC codes and then construct NBLDPC cycle codes of large girth based on circulants and finite fields by randomly choosing the nonzero field elements in their parity-check matrices. For enlarging the girth values, our approach is twofold. First, we give an exhaustive search of circulants with column/row weight ρ and design a masking matrix with good cycle distribution based on the edge-node relation in undirected graphs. Second, according to the designed masking matrix, we construct the exponent matrix based on finite fields. The iterative decoding performances of the constructed codes on the additive white Gaussian noise (AWGN) channel are finally provided.
Highlights
Nonbinary low-density parity-check (NBLDPC) codes based on modulo arithmetics were first discovered by Gallager in1960s [1] and redefined over finite fields GF ðqÞ by Davey and MacKay in 1998 [2]
As an important cycle codes, ð2, ρÞregular NBLDPC codes perform well under iterative decoding; lots of methods for constructing such codes were proposed [14,15,16,17]. Among these works on the construction of NBLDPC codes, the codes can be mainly classified into two categories: the first one is constructed by means of computer search under the algorithms satisfying certain rules, and the other one is constructed based on combinatorial designs, graph theory, matrix theory, and finite fields [18]
This paper proposed a design framework of binary QCLDPC cycle codes and constructed nonbinary LDPC
Summary
Nonbinary low-density parity-check (NBLDPC) codes based on modulo arithmetics were first discovered by Gallager in. As an important cycle codes, ð2, ρÞregular NBLDPC codes perform well under iterative decoding; lots of methods for constructing such codes were proposed [14,15,16,17]. Among these works on the construction of NBLDPC codes, the codes can be mainly classified into two categories: the first one is constructed by means of computer search under the algorithms satisfying certain rules, and the other one is constructed based on combinatorial designs, graph theory, matrix theory, and finite fields [18]. Design of NBLDPC cycle codes with large girth is proposed, and numerical results are provided .
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