An LDPC code is called ultra-sparse if its parity-check matrix has uniform column weight 2. A class of non-binary ultra-sparse quasi-cyclic LDPC (UQ-LDPC) codes with girth 12 is constructed. These codes have simple structures and very fast encoding. With iterative decoding based on the belief propagation algorithm, simulation results show that the non-binary UQ-LDPC codes significantly outperform the non-binary ultra-sparse random LDPC codes with the same parameters in certain cases.
An LDPC code is called ultra-sparse if its parity-check matrix has uniform column weight 2. A class of non-binary ultra-sparse quasi-cyclic LDPC (UQ-LDPC) codes with girth 12 is constructed. These codes have simple structures and very fast encoding. With iterative decoding based on the belief propagation algorithm, simulation results show that the non-binary UQ-LDPC codes significantly outperform the non-binary ultra-sparse random LDPC codes with the same parameters in certain cases.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
A non-binary LDPC codes whose parity check matrix has uniform column weight 2 is constructed in this paper. The approach derives a non-binary LDPC codes from a column-weight 2 binary LDPC codes which is designed according to a all one (2, k) matrix, We proposed a search algorithm for constructing a (2, k) LDPC codes with desired girth, and in this paper, we use the search algorithm twice to obtain a code with larger girth. The simulation result shows that the proposed LDPC codes outperform the random codes.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
In this paper, we propose a novel and simple construction of regular LDPC codes using sparse binary sequences. The distribution matrix of ones in a parity-check matrix is introduced into this new construction. The cyclic cross correlation function and the cyclic auto correlation function are employed to ensure that the girth of Tanner graph is at least eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.
A novel and simple construction of regular LDPC codes was proposed, which used sparse binary sequences, through studying construction methods of LDPC codes. The distribution matrix of ones in parity-check matrix was introduced into the new construction. The cyclic cross correlation function and the cyclic auto correlation function were utilized to ensure that the girth of Tanner graph was eight. The new codes perform well using the sum-product algorithm for iterative decoding. Low encoding complexity can also be achieved due to the inherent quasi-cyclic structure of the LDPC codes.
Non-binary (NB) low-density parity-check (LDPC) codes offer superior error-correcting performance compared to binary LDPC codes, especially for short and medium lengths. Constructing such codes with large girth remains challenging due to various combinatorial constraints. We present a novel algebraic and graph-theoretic construction of non-binary quasi-cyclic (QC) LDPC codes with column weight two and girth 12, which is known to be largest achievable girth for array-based QC-LDPC codes. In constructing girth-12 (2, dc) NB-QC-LDPC codes, our method attains the minimum possible code length for dc < 10. Motivated by the fact that non-binary spatially coupled (SC) QC-LDPC codes achieve optimal performance at column weight three, we further construct NB-SC-QC-LDPC codes with girth ≥ 8 while effectively reducing the number of 8-cycles. Specifically, for (3, dc) codes, our design eliminates dominant absorbing sets such as the (3, 3) and (4, 2), eliminates the (5, 1) elementary absorbing sets (EAS), and eliminates almost all (6, 2) EAS, thereby directly enhancing the error-correction performance. The proposed NB-QC-LDPC codes achieve performance comparable to NB-LDPC codes used in the BeiDou satellite navigation system, while requiring a significantly smaller parity-check matrix storage footprint, for instance, around a 44× reduction in storage requirements with respect to BeiDou rate-1/2 (88, 44) code. Also, the proposed rate-1/2 code with length n = 684 provide a 0.4 dB gain over non-binary near-regular QC-LDPC code with same parameters proposed by Huang et al. [IEEE Trans. Commun.] while requiring a smaller parity-check matrix storage footprint. Furthermore, the proposed rate-1/2 NB-SC-QC-LDPC code having length n = 4608 achieve 0.1 dB coding gain compared to existing protograph constructions while requiring a significantly smaller parity-check matrix storage footprint, i.e., around a 192× reduction.