A combining method of quasi-cyclic LDPC codes by the chinese remainder theorem (original) (raw)
Related papers
Performance Analysis of Quasi-Cyclic Low Density Parity Check Codes
Low-Density Parity-Check codes are the class of linear block codes, which perform the near Shannon limit performance on data transmission. Here, Quasi Cyclic codes are circulant permutation matrices, for the efficient encoding purpose. In this paper, QC-LDPC Codes have significant performance improvement due to the effective iterative Min-Sum decoding algorithm in terms of Bit Error Rate (BER) versus E b /N o with low and high code rates compared to other existing codes. Soft decision decoding and increased number of iterations of QC-LDPC codes has better performance.
Quasi-Cyclic LDPC Codes based on
2014
Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared to one-step circulant-based liftings. The expected performance improvement is verified by simulation results.
A subtraction based method for the construction of quasi-cyclic LDPC codes of girth eight
2016 International Siberian Conference on Control and Communications (SIBCON), 2016
This article presents a simple, less computational complexity method for constructing exponent matrix () 3, K having girth at least 8 of quasicyclic low-density parity-check (QC-LDPC) codes based on subtraction method. The construction of code deals with the generation of exponent matrix by three formulas. This method is flexible for any block-column length K. The simulations are shown in comparison with some existing appreciable work. The codes with girth 8 are constructed with circulant permutation matrix (CPM) size
Decoding of quasi-cyclic LDPC codes with section-wise cyclic structure
2014 Information Theory and Applications Workshop (ITA), 2014
Presented in this paper is a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) LDPC codes. This decoding scheme is devised based on the section-wise cyclic structure of the parity-check matrix of a QC-LDPC code. Using this decoding scheme, the hardware implementation complexity of a QC-LDPC decoder can be significantly reduced without performance degradation. A high-rate QC-LDPC code that can achieve a very low error-rate without a visible error-floor is used to demonstrate the effectiveness of the proposed decoding scheme. Also presented in this paper are two other high-rate QC-LDPC codes and a method for constructing rate-1 2 QC-LDPC codes whose Tanner graphs have girth 8. All the codes constructed perform well with low error-floor using the proposed decoding scheme.
An efficient encoding-decoding of large girth LDPC codes based on quasi-cyclic
Australian Journal of Basic and …, 2009
In this paper, we propose a novel method for constructing quasi-cyclic low-density parity check (QC-LDPC) codes based row division method which can guarantee a concentrated node degree distribution with large girth. The main advantage is that large girth QC-LDPC codes can be easily constructed with a variety of block lengths and rates. Simulation results show that the proposed codes perform significantly better than the randomly constructed codes.
Quasi-Cyclic LDPC Codes for Fast Encoding
IEEE Transactions on Information Theory, 2005
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.
Quasi-cyclic generalized ldpc codes with low error floors
IEEE Transactions on Communications, 2008
In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.
Newly Designed Quasi-Cyclic Low Density Parity Check Codes
2009
This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight which has cut down hardware implementation cost and complexity as compared to the connection of individual columns and rows. The construction of newly obtained codes gives a class of efficiently encodable quasi-cyclic LDPC codes. Index Terms--Fractional bandwidth, girth, QC-LDPC, PBNJ.
Construction of Irregular LDPC Codes by Quasi-Cyclic Extension
IEEE Transactions on Information Theory, 2000
In this correspondence, we propose an approach to construct irregular low-density parity-check (LDPC) codes based on quasi-cyclic extension. When decoded iteratively, the constructed irregular LDPC codes exhibit a relatively low error floor in the high signal-to-noise ratio (SNR) region and are subject to relatively few undetected errors. The LDPC codes constructed based on the proposed scheme remain efficiently encodable.
This paper presents a different decoding techniques for Quasi - Cyclic (QC) Low Density Parity Check (LDPC) code. QC - LDPC code is proposed to reduce the complexity of the Low Density Parity Check code while obtaining the similar performance. The encoding and decoding processes of these codes are easy to simplify and implement. The algorithm used for encoding and decoding are based on matrices and implemented on MATLAB for simulation results. In this paper decoding technique QC - LDPC is introduced a nd compare the performance of LDPC and QC - LDPC. The decoding techniques is conducted by different algorithms such as Bit Flipping (BF), Belief Propagation (BP) Log, Belief Propagation (BP) Probabilistic (Prob), Belief Propagation (BP) Log Simple.