A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.In this paper,a novel method based on Column-Difference Search Algorithm and Progressive Edge Growth Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CP-LDPC code has linear encoding complexity.The experimental results show that CP-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.35dB-3.95dB.
In this paper,a novel method based on Column-Difference Search Algorithm and Iterative Filled Algorithm is proposed to design Quasi-Cyclic LDPC codes with arbitrary girth and code rate.Due to its almost lower triangular form,CI-LDPC code has linear encoding complexity.The experimental results show that CI-LDPC codes perform better than Tanner codes and Array codes,which are another two classical QC-LDPC codes,and random codes.The code in this paper outperforms random code,Tanner code and Array code by 1.4dB～3.8dB.
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.
There is an important breakthrough in the field of forward error correction techniques, low-density parity-check (LDPC) codes. These codes have potential to approach the Shannon limit with reliable performance on a given channel, known as the channel capacity. Recently, researchers pay much more attention towards LDPC codes because its performance is better than Turbo codes. However, the LDPC code is the best when it is an irregular code and uses with a very large block-length. Although, the short block-length LDPC codes perform not so well, they are easy to implement in various practical applications. Therefore, there is still a demand of new development on the encoding side of LDPC codes for various ranges of code rate and code length so as to capable of using in many applications.This thesis proposes the development of quasi-cyclic (QC) LDPC codes for column weight 3. In the first part of this thesis, we propose a new construction algorithm of QC-LDPC codes for medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem (CRT). Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the maximum girth of the component codes. Simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods in terms of low error-floor, simple structure, high performance, and can reduce encoding complexity.In addition, this thesis also proposes two new construction methods for QC-LDPC codes, namely a base matrix method and a subtraction based method. A base matrix based method is a simple, less computational complexity method for constructing the exponent matrix (3, K) of girth 8, 10 and 12 of QC-LDPC codes. Another method is a subtraction method, which has a similar exponent matrix as a base matrix method and has a girth at least 8. Results indicate that the LDPC codes constructed from these two methods have flexibility for arbitrary block-column length K and have a similar BER performance if compared to existing methods.
Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.
This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.