Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in cu...Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.展开更多
The paper review the public-key cryptosystems based on the error correcting codes such as Goppa code, BCH code, RS code, rank distance code, algebraic geometric code as well as LDPC code, and made the comparative anal...The paper review the public-key cryptosystems based on the error correcting codes such as Goppa code, BCH code, RS code, rank distance code, algebraic geometric code as well as LDPC code, and made the comparative analyses of the merits and drawbacks of them. The cryptosystem based on Goppa code has high security, but can be achieved poor. The cryptosystems based on other error correcting codes have higher performance than Goppa code. But there are still some disadvantages to solve. At last, the paper produce an assumption of the Niederreiter cascade combination cryptosystem based on double public-keys under complex circumstances, which has higher performance and security than the traditional cryptosystems.展开更多
A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the we...A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.展开更多
In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary ...In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.展开更多
Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to im...Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.展开更多
The definition of good codes for error-detection is given. It is proved that a (n, k) linear block code in GF(q) are the good code for error-detection, if and only if its dual code is also. A series of new results abo...The definition of good codes for error-detection is given. It is proved that a (n, k) linear block code in GF(q) are the good code for error-detection, if and only if its dual code is also. A series of new results about the good codes for error-detection are derived. New lower bounds for undetected error probabilities are obtained, which are relative to n and k only, and not the weight structure of the codes.展开更多
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor...This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.展开更多
Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results s...Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results show that the ECC did improve the performance dramatically,with the SEU cross sections of SRAMs with ECC being at the order of 10^(-11) cm^2/bit,two orders of magnitude higher than that without ECC(at the order of 10^(-9) cm^2/bit).Also,ineffectiveness of ECC module,including 1-,2- and 3-bits errors in single word(not Multiple Bit Upsets),was detected.The ECC modules in SRAMs utilizing(12,8) Hamming code would lose work when 2-bits upset accumulates in one codeword.Finally,the probabilities of failure modes involving 1-,2- and 3-bits errors,were calcaulated at 39.39%,37.88%and 22.73%,respectively,which agree well with the experimental results.展开更多
This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shif...This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.展开更多
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum err...Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.展开更多
Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptab...Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptability of fixing techniques may vary for different types of code errors.How to choose the appropriate methods to fix different types of errors is still an unsolved problem.To this end,this paper first classifies code errors by Java novice programmers based on Delphi analysis,and compares the effectiveness of different deep learning models(CuBERT,GraphCodeBERT and GGNN)fixing different types of errors.The results indicated that the 3 models differed significantly in their classification accuracy on different error codes,while the error correction model based on the Bert structure showed better code correction potential for beginners’codes.展开更多
Semantic communication(SemCom)aims to achieve high-fidelity information delivery under low communication consumption by only guaranteeing semantic accuracy.Nevertheless,semantic communication still suffers from unexpe...Semantic communication(SemCom)aims to achieve high-fidelity information delivery under low communication consumption by only guaranteeing semantic accuracy.Nevertheless,semantic communication still suffers from unexpected channel volatility and thus developing a re-transmission mechanism(e.g.,hybrid automatic repeat request[HARQ])becomes indispensable.In that regard,instead of discarding previously transmitted information,the incremental knowledge-based HARQ(IK-HARQ)is deemed as a more effective mechanism that could sufficiently utilize the information semantics.However,considering the possible existence of semantic ambiguity in image transmission,a simple bit-level cyclic redundancy check(CRC)might compromise the performance of IK-HARQ.Therefore,there emerges a strong incentive to revolutionize the CRC mechanism,thus more effectively reaping the benefits of both SemCom and HARQ.In this paper,built on top of swin transformer-based joint source-channel coding(JSCC)and IK-HARQ,we propose a semantic image transmission framework SC-TDA-HARQ.In particular,different from the conventional CRC,we introduce a topological data analysis(TDA)-based error detection method,which capably digs out the inner topological and geometric information of images,to capture semantic information and determine the necessity for re-transmission.Extensive numerical results validate the effectiveness and efficiency of the proposed SC-TDA-HARQ framework,especially under the limited bandwidth condition,and manifest the superiority of TDA-based error detection method in image transmission.展开更多
In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case...In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case when errors occur in multi- ple channels. Importantly, we show the necessary and sufficient conditions on the existence of linear network error correction mul- ticast/broadcast/dispersion maximum distance separable （MDS） code on a matroidal error correction network.展开更多
This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding type...This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding types on communication performance.The study investigates the impact of on-off keying(OOK)and 2-pulse-position modulation(2-PPM)on the bit error rate(BER)in single-channel intensity and polarization multiplexing.Furthermore,it compares the error correction performance of low-density parity check(LDPC)and Reed-Solomon(RS)codes across different error correction coding types.The effects of unscattered photon ratio and depolarization ratio on BER are also verified.Finally,a UWOC system based on SPD is constructed,achieving 14.58 Mbps with polarization OOK multiplexing modulation and 4.37 Mbps with polarization 2-PPM multiplexing modulation using LDPC code error correction.展开更多
By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correc...By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correction codes. The basic properties of GMRD are investigated. It is proved that GMRD can characterize the error correction/detection capability of variable-rate linear network error correction codes when the source transmits the messages at several different rates.展开更多
Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correcti...Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge.In this paper,a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems.Firstly,syndrome ancillas are prepared into Bell states to detect errors caused by channel noise.We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type.Additionally,a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults,which may also introduce errors into the code block during the error detection process.Finally,analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.展开更多
Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximat...Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximate error correction scheme that performs dimension mapping operations on surface codes.This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions.Compared to previous error correction schemes,the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities.By reducing the number of ancilla qubits required for error correction,this approach achieves savings in measurement space and reduces resource consumption costs.In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping,we employ a reinforcement learning(RL)decoder based on deep Q-learning,which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization.Compared to the minimum weight perfect matching decoding,the threshold of the RL trained model reaches 0.78%,which is 56%higher and enables large-scale fault-tolerant quantum computation.展开更多
In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit c...In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits （Shor code, Steane code and five stable subcode）, it shows obvious superiority in the quantum coding efficiency and transmission efficiency.展开更多
An error tolerant hardware efficient verylarge scale integration （VLSI） architecture for bitparallel systolic multiplication over dual base, which canbe pipelined, is presented. Since this architecture has thefeatur...An error tolerant hardware efficient verylarge scale integration （VLSI） architecture for bitparallel systolic multiplication over dual base, which canbe pipelined, is presented. Since this architecture has thefeatures of regularity, modularity and unidirectionaldata flow, this structure is well suited to VLSIimplementations. The length of the largest delay pathand area of this architecture are less compared to the bitparallel systolic multiplication architectures reportedearlier. The architecture is implemented using Austria Micro System＇s 0.35 μm CMOS （complementary metaloxide semiconductor） technology. This architecture canalso operate over both the dual-base and polynomialbase.展开更多
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)Joint Fund of Natural Science Foundation of Shandong Province(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key R&D Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation.However,the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution.Therefore,quantum error correction technology is crucial to achieving reliable quantum computing.In this work,we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors.However,errors can occur not only in data qubits but also in syndrome qubits,and different types of errors may generate the same syndromes,complicating the decoding task and creating a need for more efficient decoding methods.To address this challenge,we used a transformer decoder based on an attention mechanism.By mapping the surface code lattice,the decoder performs a self-attention process on all input syndromes,thereby obtaining a global receptive field.The performance of the decoder was evaluated under a phenomenological error model.Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%.Additionally,we obtained decoding thresholds of 5%and 6.05%at maximum code distances of 7 and 9,respectively.These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.
基金Supported by the Postgraduate Project of Military Science of PLA(2013JY431)55th Batch of China Postdoctoral Second-Class on Fund Projects(2014M552656)
文摘The paper review the public-key cryptosystems based on the error correcting codes such as Goppa code, BCH code, RS code, rank distance code, algebraic geometric code as well as LDPC code, and made the comparative analyses of the merits and drawbacks of them. The cryptosystem based on Goppa code has high security, but can be achieved poor. The cryptosystems based on other error correcting codes have higher performance than Goppa code. But there are still some disadvantages to solve. At last, the paper produce an assumption of the Niederreiter cascade combination cryptosystem based on double public-keys under complex circumstances, which has higher performance and security than the traditional cryptosystems.
基金Sponsored by the Ministerial Level Advanced Research Foundation (20304)
文摘A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.
文摘In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072071)
文摘Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
文摘The definition of good codes for error-detection is given. It is proved that a (n, k) linear block code in GF(q) are the good code for error-detection, if and only if its dual code is also. A series of new results about the good codes for error-detection are derived. New lower bounds for undetected error probabilities are obtained, which are relative to n and k only, and not the weight structure of the codes.
基金Supported by Trans-century Training Program Foundation for the Talents by the State Education Commission
文摘This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.
基金Supported by the National Natural Science Foundation of China(Nos.11079045 and 11179003)the Important Direction Project of the CAS Knowledge Innovation Program(No.KJCX2-YW-N27)
文摘Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results show that the ECC did improve the performance dramatically,with the SEU cross sections of SRAMs with ECC being at the order of 10^(-11) cm^2/bit,two orders of magnitude higher than that without ECC(at the order of 10^(-9) cm^2/bit).Also,ineffectiveness of ECC module,including 1-,2- and 3-bits errors in single word(not Multiple Bit Upsets),was detected.The ECC modules in SRAMs utilizing(12,8) Hamming code would lose work when 2-bits upset accumulates in one codeword.Finally,the probabilities of failure modes involving 1-,2- and 3-bits errors,were calcaulated at 39.39%,37.88%and 22.73%,respectively,which agree well with the experimental results.
文摘This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.
基金the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Project of Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.
基金supported in part by the Education Department of Sichuan Province(Grant No.[2022]114).
文摘Automatically correcting students’code errors using deep learning is an effective way to reduce the burden of teachers and to enhance the effects of students’learning.However,code errors vary greatly,and the adaptability of fixing techniques may vary for different types of code errors.How to choose the appropriate methods to fix different types of errors is still an unsolved problem.To this end,this paper first classifies code errors by Java novice programmers based on Delphi analysis,and compares the effectiveness of different deep learning models(CuBERT,GraphCodeBERT and GGNN)fixing different types of errors.The results indicated that the 3 models differed significantly in their classification accuracy on different error codes,while the error correction model based on the Bert structure showed better code correction potential for beginners’codes.
基金supported in part by the National Key Research and Development Program of China under Grant 2024YFE0200600in part by the National Natural Science Foundation of China under Grant 62071425+3 种基金in part by the Zhejiang Key Research and Development Plan under Grant 2022C01093in part by the Zhejiang Provincial Natural Science Foundation of China under Grant LR23F010005in part by the National Key Laboratory of Wireless Communications Foundation under Grant 2023KP01601in part by the Big Data and Intelligent Computing Key Lab of CQUPT under Grant BDIC-2023-B-001.
文摘Semantic communication(SemCom)aims to achieve high-fidelity information delivery under low communication consumption by only guaranteeing semantic accuracy.Nevertheless,semantic communication still suffers from unexpected channel volatility and thus developing a re-transmission mechanism(e.g.,hybrid automatic repeat request[HARQ])becomes indispensable.In that regard,instead of discarding previously transmitted information,the incremental knowledge-based HARQ(IK-HARQ)is deemed as a more effective mechanism that could sufficiently utilize the information semantics.However,considering the possible existence of semantic ambiguity in image transmission,a simple bit-level cyclic redundancy check(CRC)might compromise the performance of IK-HARQ.Therefore,there emerges a strong incentive to revolutionize the CRC mechanism,thus more effectively reaping the benefits of both SemCom and HARQ.In this paper,built on top of swin transformer-based joint source-channel coding(JSCC)and IK-HARQ,we propose a semantic image transmission framework SC-TDA-HARQ.In particular,different from the conventional CRC,we introduce a topological data analysis(TDA)-based error detection method,which capably digs out the inner topological and geometric information of images,to capture semantic information and determine the necessity for re-transmission.Extensive numerical results validate the effectiveness and efficiency of the proposed SC-TDA-HARQ framework,especially under the limited bandwidth condition,and manifest the superiority of TDA-based error detection method in image transmission.
基金Supported by the National Natural Science Foundation of China(6127117461272492)
文摘In this paper, we further study the connections between linear network error correction codes and representable matroids. We extend the concept of matroidal network introduced by Dougherty et al. to a generalized case when errors occur in multi- ple channels. Importantly, we show the necessary and sufficient conditions on the existence of linear network error correction mul- ticast/broadcast/dispersion maximum distance separable （MDS） code on a matroidal error correction network.
基金supported in part by the National Natural Science Foundation of China(Nos.62071441 and 61701464)in part by the Fundamental Research Funds for the Central Universities(No.202151006).
文摘This study explores the application of single photon detection(SPD)technology in underwater wireless optical communication(UWOC)and analyzes the influence of different modulation modes and error correction coding types on communication performance.The study investigates the impact of on-off keying(OOK)and 2-pulse-position modulation(2-PPM)on the bit error rate(BER)in single-channel intensity and polarization multiplexing.Furthermore,it compares the error correction performance of low-density parity check(LDPC)and Reed-Solomon(RS)codes across different error correction coding types.The effects of unscattered photon ratio and depolarization ratio on BER are also verified.Finally,a UWOC system based on SPD is constructed,achieving 14.58 Mbps with polarization OOK multiplexing modulation and 4.37 Mbps with polarization 2-PPM multiplexing modulation using LDPC code error correction.
文摘By extending the notion of the minimum distance for linear network error correction code(LNEC), this paper introduces the concept of generalized minimum rank distance(GMRD) of variable-rate linear network error correction codes. The basic properties of GMRD are investigated. It is proved that GMRD can characterize the error correction/detection capability of variable-rate linear network error correction codes when the source transmits the messages at several different rates.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61671087 and 61962009)the Fundamental Research Funds for the Central Universities,China(Grant No.2019XD-A02)+1 种基金Huawei Technologies Co.Ltd(Grant No.YBN2020085019)the Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data(Grant No.2018BDKFJJ018)。
文摘Fault-tolerant error-correction(FTEC)circuit is the foundation for achieving reliable quantum computation and remote communication.However,designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge.In this paper,a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems.Firstly,syndrome ancillas are prepared into Bell states to detect errors caused by channel noise.We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into X-type and Z-type.Additionally,a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults,which may also introduce errors into the code block during the error detection process.Finally,analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2021MF049,ZR2022LLZ012,and ZR2021LLZ001)。
文摘Quantum error correction technology is an important method to eliminate errors during the operation of quantum computers.In order to solve the problem of influence of errors on physical qubits,we propose an approximate error correction scheme that performs dimension mapping operations on surface codes.This error correction scheme utilizes the topological properties of error correction codes to map the surface code dimension to three dimensions.Compared to previous error correction schemes,the present three-dimensional surface code exhibits good scalability due to its higher redundancy and more efficient error correction capabilities.By reducing the number of ancilla qubits required for error correction,this approach achieves savings in measurement space and reduces resource consumption costs.In order to improve the decoding efficiency and solve the problem of the correlation between the surface code stabilizer and the 3D space after dimension mapping,we employ a reinforcement learning(RL)decoder based on deep Q-learning,which enables faster identification of the optimal syndrome and achieves better thresholds through conditional optimization.Compared to the minimum weight perfect matching decoding,the threshold of the RL trained model reaches 0.78%,which is 56%higher and enables large-scale fault-tolerant quantum computation.
基金Supported by the National Natural Science Foundation of China (61271122)the Natural Science Foundation of Anhui Province(1208085MF102)
文摘In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits （Shor code, Steane code and five stable subcode）, it shows obvious superiority in the quantum coding efficiency and transmission efficiency.
文摘An error tolerant hardware efficient verylarge scale integration （VLSI） architecture for bitparallel systolic multiplication over dual base, which canbe pipelined, is presented. Since this architecture has thefeatures of regularity, modularity and unidirectionaldata flow, this structure is well suited to VLSIimplementations. The length of the largest delay pathand area of this architecture are less compared to the bitparallel systolic multiplication architectures reportedearlier. The architecture is implemented using Austria Micro System＇s 0.35 μm CMOS （complementary metaloxide semiconductor） technology. This architecture canalso operate over both the dual-base and polynomialbase.
