QC-LDPC Codes Construction by Concatenating of Circulant Matrices as Block- Columns Mohammad Hesam Tadayon Iran Telecommunication Research Center (ITRC) Tehran, Iran tadayon@itrc.ac.ir Mohammad Mohammadi Malek-Ashtar University Isfahan, Iran Amohamadi70@gmail.com Received: June 14, 2015- Accepted: March 17, 2016 Abstract—In this paper a new low complexity method for constructing binary quasi-cyclic low-density parity-check (QC-LDPC) codes is introduced. In the proposed method, each block-column of the parity check matrix H is made by a circulant matrix in a way that the associated Tanner graph is free of cycle four. Each circulant matrix in H is made by a generator column. The generator columns should be selected in a way that each associated circulant matrix and every two distinct circulant matrices are free of cycle four. The generator columns are made by row distance sets. An algorithm for generating distance sets and obtaining circulant matrices with columns of weight three is presented separately. Simplicity of construction and having a good flexible family of quasi cyclic LDPC codes both in rate and length are the main properties of the proposed method. The performance of the proposed codes is compared with that of the random-like and Array LDPC codes over an AWGN channel. Simulation results show that from the performance perspective, the constructed codes are competitive with random-like and Array LDPC codes. Keywords- QC-LDPC codes, girth, circulant matrices, AWGN channel, concatenation. I. INTRODUCTION QC-LDPC codes are a family of capacity- approaching and high performance error correcting linear codes [1, 2]. Construction of these codes is divided into two categories: random-like codes, such as [1, 2] and structured codes, such as [3-12]. As mentioned in many papers, the encoding complexity of quasi-cyclic codes is extremely low [3-5]. In general, QC-LDPC codes are constructed by two main methods: superposition techniques [4, 9] and parity check matrices derived by circulant matrices [6, 8]. The proposed method in this paper can produce QC- LDPC codes with different lengths and rates. A parity check matrix H has been constructed by concatenation of circulant matrices as block-columns. Each circulant matrix is constructed by a generator column with an arbitrary considered weight. We must take an order on nonzero elements of each generator column such that each associated circulant matrix and every two disjoint circulant matrices be free of cycle four. Therefore the associated Tanner graph of parity check matrix H will have girth at least six. Constructed quasi-cyclic LDPC codes in this paper can have arbitrary column weights, lengths and rates. Therefore the main task in this paper is to construct appropriate generator columns. We have introduced a method of constructing particular sets, known as row distance sets, which are used for constructing generator columns. Furthermore, we represent generator columns by generator polynomials that demonstrate a simple exhibition of H. The performance of the proposed codes on an AWGN channel by sum-product algorithm (SPA) decoding is examined and compared with that of the random-like and Array LDPC codes as well-known QC-LDPC codes [13]. Simulation results show that the constructed Downloaded from journal.itrc.ac.ir at 15:48 IRST on Thursday February 18th 2021