Doped low-density parity-check codes

In this paper,we propose a doping approach to lower the error floor of Low-Density Parity-Check(LDPC)codes.The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code.Accordingly,an algorithm for selecting the information bits of the short code is proposed,and a specific two-stage decoding algorithm is presented.Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10^(-6)Furthermore,the proposed design can lower the error floor of original LDPC Codes.

Low-Density Parity-Check Codes for Noncoherent UWB Communication Systems

In order to guarantee reliable data transmission, powerful channel coding techniques are usually required in noncoherent ultra-wideband(UWB) communication systems. Accordingly, several forward error correction(FEC) codes, such as Reed-Solomon and convolutional codes have been used in noncoherent UWB systems to improve the bit error rate(BER) performance. In this paper, low-density parity-check(LDPC) codes are further studied as more powerful FEC candidates for noncoherent UWB systems. Two LDPC codes and the corresponding decoding procedures are presented for noncoherent UWB systems. Moreover, performance comparison between the LDPC codes and other FEC codes are provided for three major noncoherent UWB communication systems, namely, noncoherent pulse position modulation(NC-PPM), transmitted reference(TR) and transmitted reference pulse cluster(TRPC). Both theoretical analysis and simulation results show that the two investigated LDPC codes outperform other existing FEC codes with limited penalty in terms of complexity and therefore they are promising FEC candidates for noncoherent UWB systems with low-cost and low-power consumption.

THE Q-MATRIX LOW-DENSITY PARITY-CHECK CODES

This paper presents a matrix permuting approach to the construction of Low-Density Parity-Check (LDPC) code. It investigates the structure of the sparse parity-check matrix defined by Gallager. It is discovered that the problem of constructing the sparse parity-check matrix requires an algorithm that is efficient in search environments and also is able to work with constraint satisfaction problem. The definition of Q-matrix is given, and it is found that the queen algorithm enables to search the Q-matrix. With properly permuting Q-matrix as sub-matrix, the sparse parity-check matrix which satisfied constraint condition is created, and the good regular-LDPC code that is called the Q-matrix LDPC code is generated. The result of this paper is significant not only for designing low complexity encoder, improving performance and reducing complexity of iterative decoding arithmetic, but also for building practical system of encodable and decodable LDPC code.

Low-Density Parity-Check Codes:Highway to Channel Capacity

Low-density parity-check(LDPC)codes are not only capacity-approaching,but also greatly suitable for high-throughput implementation.Thus,they are the most popular codes for high-speed data transmission in the past two decades.Thanks to the low-density property of their parity-check matrices,the optimal maximum a posteriori probability decoding of LDPC codes can be approximated by message-passing decoding with linear complexity and highly parallel nature.Then,it reveals that the approximation has to carry on Tanner graphs without short cycles and small trapping sets.Last,it demonstrates that well-designed LDPC codes with the aid of computer simulation and asymptotic analysis tools are able to approach the channel capacity.Moreover,quasi-cyclic(QC)structure is introduced to significantly facilitate their high-throughput implementation.In fact,compared to the other capacity-approaching codes,QC-LDPC codes can provide better area-efficiency and energy-efficiency.As a result,they are widely applied in numerous communication systems,e.g.,Landsat satellites,Chang’e Chinese Lunar mission,5G mobile communications and so on.What’s more,its extension to non-binary Galois fields has been adopted as the channel coding scheme for BeiDou navigation satellite system.

REGULAR LOW-DENSITY PARITY-CHECK CODES BASED ON SHIFTED IDENTITY MATRICES

This paper extends the class of Low-Density Parity-Check (LDPC) codes that can be constructed from shifted identity matrices. To construct regular LDPC codes, a new method is proposed. Two simple inequations are adopted to avoid the short cycles in Tanner graph, which makes the girth of Tanner graphs at least 8. Because their parity-check matrices are made up of circulant matrices, the new codes are quasi-cyclic codes. They perform well with iterative decoding.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

Low-Complexity Optimization Algorithm for Irregular Low-Density Parity-Check Codes

A low-complexity algorithm is proposed in this paper in order to optimize irregular low-density parity-check （LDPC） codes.The algorithm proposed can calculate the noise threshold by means of a one-dimensional density evolution and search the optimal degree profiles with fast-convergence differential evolution,so that it has a lower complexity and a faster convergence speed.Simulation resuits show that the irregular LDPC codes optimized by the presented algorithm can also perform better than Turbo codes at moderate block length even with less computation cost.

Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

Implementation of low-density parity-check codes decoder for CCSDS standard

The complexity/performance balanced decoder for low-density parity-check （LDPC） codes is preferred in practical wireless communication systems. A low complexity LDPC decoder for the Consultative Committee for Space Data Systems （CCSDS） standard is achieved in DSP. An ap- proximate decoding algorithm, normalized rain-sum algorithm, is used in the implementation for its low amounts of computation. To reduce the performance loss caused by the approximation, the pa- rameters of the normalized min-sum algorithm are determined by calculating and finding the mini- mum value of thresholds through density evolution. The minimum value which indicates the best per- formance of the decoding algorithm is corresponding with the optimized parameters. In implementa- tion, the memory cost is saved by decomposing the parity-check matrix into submatrices to store and the computation of passing message in decoding is accelerated by using the intrinsic function of DSP. The performance of the decoder with optimized factors is simulated and compared with the ideal BP decoder. The result shows they have about the same performance.

Construction of Quasi-Cyclic Low-Density Parity-Check Codes for Simplifying Shuffle Networks in Layered Decoder

Offset Shuffle Networks(OSNs) interleave a-posterior probability messages in the Block Row-Layered Decoder(BRLD) of QuasiCyclic Low-Density Parity-Check(QC-LDPC)codes.However,OSNs usually consume a significant amount of computational resources and limit the clock frequency,particularly when the size of the Circulant Permutation Matrix(CPM)is large.To simplify the architecture of the OSN,we propose a Simplified Offset Shuffle Network Block Progressive Edge-Growth(SOSNBPEG) algorithm to construct a class of QCLDPC codes.The SOSN-BPEG algorithm constrains the shift values of CPMs and the difference of the shift values in the same column by progressively appending check nodes.Simulation results indicate that the error performance of the SOSN-BPEG codes is the same as that of the codes in WiMAX and DVB-S2.The SOSNBPEG codes can reduce the complexity of the OSNs by up to 54.3%,and can improve the maximum frequency by up to 21.7%for various code lengths and rates.

Code Optimization, Frozen Glassy Phase and Improved Decoding Algorithms for Low-Density Parity-Check Codes

The statistical physics properties of low-density parity-cheek codes for the binary symmetric channel are investigated as a spin glass problem with multi-spin interactions and quenched random fields by the cavity method. By evaluating the entropy function at the Nishimori temperature, we find that irregular constructions with heterogeneous degree distribution of check （bit） nodes have higher decoding thresholds compared to regular counterparts with homo- geneous degree distribution. We also show that the instability of the mean-field caiculation takes place only after the entropy crisis, suggesting the presence of a frozen glassy phase at low temperatures. When no prior knowledge of channel noise is assumed （searching for the ground state）, we find that a reinforced strategy on normal belief propagation will boost the decoding threshold to a higher value than the normal belief propagation. This value is dose to the dynamicai transition where all local search heuristics fail to identify the true message （codeword or the ferromagnetic state）. After the dynamical transition, the number of metastable states with larger energy density （than the ferromagnetic state） becomes exponentially numerous. When the noise level of the transmission channel approaches the static transition point, there starts to exist exponentiaily numerous codewords sharing the identical ferromagnetic energy.

Efficient unequal error protection for online fountain codes

In this paper,an efficient unequal error protection(UEP)scheme for online fountain codes is proposed.In the buildup phase,the traversing-selection strategy is proposed to select the most important symbols(MIS).Then,in the completion phase,the weighted-selection strategy is applied to provide low overhead.The performance of the proposed scheme is analyzed and compared with the existing UEP online fountain scheme.Simulation results show that in terms of MIS and the least important symbols(LIS),when the bit error ratio is 10-4,the proposed scheme can achieve 85%and 31.58%overhead reduction,respectively.

Minimum distances of three families of low-density parity-check codes based on finite geometries

Three families of low-density parity-check （LDPC） codes are constructed based on the totally isotropic subspaces of symplectic, unitary, and orthogonal spaces over finite fields, respectively. The minimum distances of the three families of LDPC codes in some special cases are settled.

CodeScore-R:用于评估代码合成功能准确性的自动化鲁棒指标

评估指标在代码合成领域中至关重要.常用的代码评估指标可以分为3种类型:基于匹配、基于语义和基于执行.其中,基于执行的Pass@k指标通过执行测试用例,能够准确判断预测代码的功能准确性.然而,该指标的计算需要大量开销,因此亟需设计一种自动化评估指标,在无需测试用例时仍可评估预测代码的功能准确性.此外,好的评估指标应当具有鲁棒性,即预测代码发生微小改变时,评估指标仍能保持其准确性.为此,提出了一种基于UniXcoder和对比学习的自动化鲁棒指标CodeScore-R,用于评估代码合成的功能准确性. CodeScore-R采用草图化处理、语法等价转换和变异测试等技术手段,有效减轻了标识符、语法结构和运算符对评估结果的干扰.实验结果表明,在Java和Python语言上的代码生成和迁移任务中,CodeScore-R的表现优于其他无需测试用例的评估指标,且更接近Pass@k指标,并具有更强的鲁棒性.

Belief-Propagation-Approximated Decoding of Low-Density Parity-Check Codes

In this paper, we propose a new reduced-complexity decoding algorithm of Low-Density Parity-Check (LDPC) codes, called Belief-Propagation-Approximated (BPA) algorithm, which utilizes the idea of normalization and translates approximately the intricate nonlinear operation in the check nodes of the original BP algorithm to only one operation of looking up the table. The normalization factors can be obtained by simulation, or theoretically. Simulation results demonstrate that BPA algorithm exhibits fairly satisfactory bit error performance on the Additive White Gaussian Noise (AWGN) channel.

Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

Quantum quasi-cyclic low-density parity-check error-correcting codes

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic （QC） low-density parity-check （LDPC） codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated.

Novel modified min-sum decoding algorithm for low-density parity-check codes

The problem of improving the performance of min-sum decoding of low-density parity-check （LDPC） codes is considered in this paper. Based on min-sum algorithm, a novel modified min-sum decoding algorithm for LDPC codes is proposed. The proposed algorithm modifies the variable node message in the iteration process by averaging the new message and previous message if their signs are different. Compared with the standard min-sum algorithm, the modification is achieved with only a small increase in complexity, but significantly improves decoding performance for both regular and irregular LDPC codes. Simulation results show that the performance of our modified decoding algorithm is very close to that of the standard sum-product algorithm for moderate length LDPC codes.

Replica horizontal-shuffled iterative decoding of low-density parity-check codes

For practical considerations,it is essential to accelerate the convergence speed of the decoding algorithm used in an iterative decoding system. In this paper,replica versions of horizontal-shuffled decoding algorithms for low-density parity-check （LDPC） codes are proposed to improve the convergence speed of the original versions. The extrinsic information transfer （EXIT） chart technique is extended to the proposed algorithms to predict their convergence behavior. Both EXIT chart analysis and numerical results show that replica plain horizontal-shuffled （RPHS） decoding converges much faster than both plain horizontal-shuffled （PHS） decoding and the standard belief-propagation （BP） decoding. Furthermore,it is also revealed that replica group horizontal-shuffled （RGHS） decoding can increase the parallelism of RPHS decoding as well as preserve its high convergence speed if an equivalence condition is satisfied,and is thus suitable for hardware implementation.

Blind Recognition of Non-Binary LDPC Codes Based on Ant Colony Optimization

This paper introduces a novel blind recognition of non-binary low-density parity-check(LDPC)codes without a candidate set,using ant colony optimization(ACO)algorithm over additive white Gaussian noise(AWGN)channels.Specifically,the scheme that effectively combines the ACO algorithm and the non-binary elements over finite fields is proposed.Furthermore,an improved,simplified elitist ACO algorithm based on soft decision reliability is introduced to recognize the parity-check matrix over noisy channels.Simulation results show that the recognition rate continuously increases with an increased signalto-noise ratio(SNR)over the AWGN channel.