Quaternary quasi-cyclic codes

Quasi-cyclic codes of length mn over Z4 are shown to be equivalent to A-submodules of A^n, where A = Z4[x]/（x^m - 1）. In the case of m being odd, all quasi-cyclic codes are shown to be decomposable into the direct sum of a fixed number of cyclic irreducible A-submodules. Finally the distinct quasi-cyclic codes as well as some specific subclasses are enumerated.

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.

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.

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.

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.

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.

Quantized Decoders that Maximize Mutual Information for Polar Codes

In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss.

Decoding topological XYZ^(2) codes with reinforcement learning based on attention mechanisms

Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.

Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

Several Classes of Two-weight or Three-weight Linear Codes and Their Applications

Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].

Polar codes based OFDM-PLC systems in the presence of impulsive noise

Power line communication(PLC)has the potential to become the preferred technique for providing broadband communication to homes and offices with advantage of eliminating the need for new wiring infrastructure and reducing the cost.But it suffers from the impulsive noise because it introduces significant time variance into the power line channel.In this paper,a polar codes based orthogonal frequency division multiplexing(OFDM)PLC system is proposed to deal with the impulsive noise and thereby improve the transmission performance.Firstly,the impulsive noise is modelled with a multi-damped sine function by analyzing the time behavior of impulse events.Then the polar codes are used to combat the impulsive noise of PLC channel,and a low complexity bit-flipping decoding method based on CRC-aided successive cancellation list(CA-SCL)decoding algorithm is proposed.Simulations evaluate the proposed decoding algorithm and the results validate the suggested polar codes based OFDM-PLC scheme which can improve the BER performance of PLC with impulsive interference.

1-GENERATOR QUASI-CYCLIC CODES

This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.

DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES

A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.

Combinatorial design-based quasi-cyclic LDPC codes with girth eight

This paper presents a novel regular Quasi-Cyclic (QC)Low Density Parity Check (LDPC)codes with columnweight three and girth at least eight.These are designed on the basis of combinatorial design in which subsets applied for the construction of circulant matrices are determined by a particular subset.Considering the nonexistence of cycles four and six in the structure of the parity check matrix,a bound for their minimum weight is proposed.The simtdations conducted confirm that without applying a masking technique,the newly implemented codes have a performance similar to or better than other well-known codes.This is evident in the waterfall region, while their error floor at very low Bit Error Rate (BER)is expected.

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.

On the Girth of Tanner (5,7) Quasi-Cyclic LDPC Codes

The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.

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.

A Golden Decade of Polar Codes:From Basic Principle to 5G Applications

After the pursuit of seventy years,the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding,which is the great breakthrough of the coding theory in the past two decades.In this survey,we retrospect the history of polar codes and summarize the advancement in the past ten years.First,the primary principle of channel polarization is investigated such that the basic construction,coding method and the classic successive cancellation(SC)decoding are reviewed.Second,in order to improve the performance of the finite code length,we introduce the guiding principle and conclude five design criteria for the construction,design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature.Especially,we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system.Furthermore,the improved SC decoding algorithms,such as SC list(SCL)decoding and SC stack(SCS)decoding etc.,are investigated and compared.Finally,the research prospects of polar codes for the future 6G communication system are explored,including the optimization of short polar codes,coding construction in fading channels,polar coded modulation and HARQ,and the polar coded transmission,namely polar processing.Predictably,as a new coding methodology,polar codes will shine a light on communication theory and unveil a revolution in transmission technology.

Open-Source Codes of Topology Optimization: A Summary for Beginners to Start Their Research

Topology optimization(TO),a numerical technique to find the optimalmaterial layoutwith a given design domain,has attracted interest from researchers in the field of structural optimization in recent years.For beginners,opensource codes are undoubtedly the best alternative to learning TO,which can elaborate the implementation of a method in detail and easily engage more people to employ and extend the method.In this paper,we present a summary of various open-source codes and related literature on TO methods,including solid isotropic material with penalization(SIMP),evolutionary method,level set method(LSM),moving morphable components/voids(MMC/MMV)methods,multiscale topology optimization method,etc.Simultaneously,we classify the codes into five levels,fromeasy to difficult,depending on their difficulty,so that beginners can get started and understand the form of code implementation more quickly.