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...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.展开更多
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
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, 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 co...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.展开更多
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 corre...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.展开更多
Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including O...Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including Orthogonal STBCs(OSTBCs),Non-Orthogonal(NOSTBCs),and Quasi-Orthogonal STBCs(QOSTBCs),do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas.This paper targets this problem and applies Maximum Rank Distance(MRD)codes in designing STBCOFDM systems.By following the direct-matrix construction method,we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas.Work uses MRD-STBCs built over Phase-Shift Keying(PSK)modulation to develop an MRD-based STBC-OFDM system.The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM.It also provides 25%higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas.The tradeoffs are minor increases in computational complexity and processing delays.展开更多
Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of...Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.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
By mcans of stable attractors of discret Hopfield neural network (DHNN) , anew class of nonlinear error control codes is sugsested and some relativetheorems are presented. A kind of single error control codes is also ...By mcans of stable attractors of discret Hopfield neural network (DHNN) , anew class of nonlinear error control codes is sugsested and some relativetheorems are presented. A kind of single error control codes is also given forillustrating this new approach.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
A novel joint source channel distortion model was proposed, which can essentially estimate the average distortion in progressive image transmission. To improve the precision of the model, the redundancy generated by a...A novel joint source channel distortion model was proposed, which can essentially estimate the average distortion in progressive image transmission. To improve the precision of the model, the redundancy generated by a forbidden symbol in the arithmetic codes is used to distinguish the quantization distortion and the channel distortion, all the coefficients from the first error one to the end of the sequence are set to be a value within the variance range of the coefficients instead of zero, then the error propagation coming from the entropy coding can be essentially estimated, which is disregarded in the most conventional joint source channel coding (JSCC) systems. The precision of the model in terms of average peak-signal-to-noise has been improved about 0.5 dB compared to classical works. An efficient unequal error protection system based on the model is developed, and can be used in the wireless communication systems.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 article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved i...In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.展开更多
In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is hom...In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is homomorphic network error-control code in network coding. That is, if the source packets at the source node for a linear network coding are precoded using a linear block code, then every packet flowing in the network regarding to the source satisfies the same constraints as the source. As a consequence, error detection and correction can be performed at every intermediate nodes of multicast flow, rather than only at the destination node in the conventional way, which can help to identify and correct errors timely at the error-corrupted link and save the cost of forwarding error-corrupted data to the destination node when the intermediate nodes are ignorant of the errors. In addition, three examples are demonstrated which show that homomorphic linear code can be combined with homomorphic signature, McEliece public-key cryptosystem and unequal error protection respectively and thus have a great potential of practical utility.展开更多
Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem s...Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.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
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
基金supported by the National Natural Science Foundation of China(61601147)the Beijing Natural Science Foundation(L182032)。
文摘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.
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.
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)。
文摘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.
基金Project supported by Natural Science Foundation of Shandong Province,China (Grant Nos.ZR2021MF049,ZR2022LLZ012,and ZR2021LLZ001)。
文摘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.
基金supported by the Excellent Foreign Student scholarship program,Sirindhorn International Institute of Technology.
文摘Space-Time Block Coded(STBC)Orthogonal Frequency Division Multiplexing(OFDM)satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel.However,conventional STBCs,including Orthogonal STBCs(OSTBCs),Non-Orthogonal(NOSTBCs),and Quasi-Orthogonal STBCs(QOSTBCs),do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas.This paper targets this problem and applies Maximum Rank Distance(MRD)codes in designing STBCOFDM systems.By following the direct-matrix construction method,we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas.Work uses MRD-STBCs built over Phase-Shift Keying(PSK)modulation to develop an MRD-based STBC-OFDM system.The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM.It also provides 25%higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas.The tradeoffs are minor increases in computational complexity and processing delays.
基金supported in part by National Nature Science Foundation of China under Grant No.61471286,No.61271004the Fundamental Research Funds for the Central Universitiesthe open research fund of Key Laboratory of Information Coding and Transmission,Southwest Jiaotong University(No.2010-03)
文摘Decoding by alternating direction method of multipliers(ADMM) is a promising linear programming decoder for low-density parity-check(LDPC) codes. In this paper, we propose a two-step scheme to lower the error floor of LDPC codes with ADMM penalized decoder.For the undetected errors that cannot be avoided at the decoder side, we modify the code structure slightly to eliminate low-weight code words. For the detected errors induced by small error-prone structures, we propose a post-processing method for the ADMM penalized decoder. Simulation results show that the error floor can be reduced significantly over three illustrated LDPC codes by the proposed two-step scheme.
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.
文摘By mcans of stable attractors of discret Hopfield neural network (DHNN) , anew class of nonlinear error control codes is sugsested and some relativetheorems are presented. A kind of single error control codes is also given forillustrating this new approach.
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The National Natural Science Foundation of China (No. 60202006)
文摘A novel joint source channel distortion model was proposed, which can essentially estimate the average distortion in progressive image transmission. To improve the precision of the model, the redundancy generated by a forbidden symbol in the arithmetic codes is used to distinguish the quantization distortion and the channel distortion, all the coefficients from the first error one to the end of the sequence are set to be a value within the variance range of the coefficients instead of zero, then the error propagation coming from the entropy coding can be essentially estimated, which is disregarded in the most conventional joint source channel coding (JSCC) systems. The precision of the model in terms of average peak-signal-to-noise has been improved about 0.5 dB compared to classical works. An efficient unequal error protection system based on the model is developed, and can be used in the wireless communication systems.
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.
文摘In this article, we study the ability of error-correcting quantum codes to increase the fidelity of quantum states throughout a quantum computation. We analyze arbitrary quantum codes that encode all qubits involved in the computation, and we study the evolution of n-qubit fidelity from the end of one application of the correcting circuit to the end of the next application. We assume that the correcting circuit does not introduce new errors, that it does not increase the execution time (i.e. its application takes zero seconds) and that quantum errors are isotropic. We show that the quantum code increases the fidelity of the states perturbed by quantum errors but that this improvement is not enough to justify the use of quantum codes. Namely, we prove that, taking into account that the time interval between the application of the two corrections is multiplied (at least) by the number of qubits n (due to the coding), the best option is not to use quantum codes, since the fidelity of the uncoded state over a time interval n times smaller is greater than that of the state resulting from the quantum code correction.
基金supported by Natural Science Foundation of China (No.61271258)
文摘In this work, the homomorphism of the classic linear block code in linear network coding for the case of binary field and its extensions is studied. It is proved that the classic linear error-control block code is homomorphic network error-control code in network coding. That is, if the source packets at the source node for a linear network coding are precoded using a linear block code, then every packet flowing in the network regarding to the source satisfies the same constraints as the source. As a consequence, error detection and correction can be performed at every intermediate nodes of multicast flow, rather than only at the destination node in the conventional way, which can help to identify and correct errors timely at the error-corrupted link and save the cost of forwarding error-corrupted data to the destination node when the intermediate nodes are ignorant of the errors. In addition, three examples are demonstrated which show that homomorphic linear code can be combined with homomorphic signature, McEliece public-key cryptosystem and unequal error protection respectively and thus have a great potential of practical utility.
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2021MF049)the Joint Fund of the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2022LLZ012 and ZR2021LLZ001)the Key Research and Development Program of Shandong Province,China(Grant No.2023CXGC010901)。
文摘Quantum error-correcting codes are essential for fault-tolerant quantum computing,as they effectively detect and correct noise-induced errors by distributing information across multiple physical qubits.The subsystem surface code with three-qubit check operators demonstrates significant application potential due to its simplified measurement operations and low logical error rates.However,the existing minimum-weight perfect matching(MWPM)algorithm exhibits high computational complexity and lacks flexibility in large-scale systems.Therefore,this paper proposes a decoder based on a graph attention network(GAT),representing error syndromes as undirected graphs with edge weights,and employing a multihead attention mechanism to efficiently aggregate node features and enable parallel computation.Compared to MWPM,the GAT decoder exhibits linear growth in computational complexity,adapts to different quantum code structures,and demonstrates stronger robustness under high physical error rates.The experimental results demonstrate that the proposed decoder achieves an overall accuracy of 89.95%under various small code lattice sizes(L=2,3,4,5),with the logical error rate threshold increasing to 0.0078,representing an improvement of approximately 13.04%compared to the MWPM decoder.This result significantly outperforms traditional methods,showcasing superior performance under small code lattice sizes and providing a more efficient decoding solution for large-scale quantum error correction.
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.
