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
Turbo code has drawn more and more attractions for high data rate transmission these years especially in W CDMA and CDMA2000 of the third generation mobile communications systems. In this paper, the simulation perfor...Turbo code has drawn more and more attractions for high data rate transmission these years especially in W CDMA and CDMA2000 of the third generation mobile communications systems. In this paper, the simulation performance of turbo code under Rayleigh fading channel and additive white Gaussian channels are depicted. Comparison with the performance of convolutional code are made respect to different parameters, such as pilot length, interleaver size, frame length, mobile velocity and data rate, etc. Faithful results are drawn out.展开更多
A new method to recover packet losses using (2,1,m) convolutional codes is proposed. The erasure correcting decoding algorithm and the decoding determinant theorem is presented. It is also proved that the codes with o...A new method to recover packet losses using (2,1,m) convolutional codes is proposed. The erasure correcting decoding algorithm and the decoding determinant theorem is presented. It is also proved that the codes with optimal distance profile have also optimal delay characteristic. Simulation results show that the proposed method can recover the packet losses more elliciently than RS codes over different decoding delay conditions and thus suits for different packet network delav conditions.展开更多
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved i...The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.展开更多
In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received w...In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.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 the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting err...In the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting errors of the channel A is presented.展开更多
In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes based on multiplicative group of finite field is prop...In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate(BER) is 10-6, in the same simulation environment, the net coding gain(NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.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 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
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
Entanglement-assisted quantum error correction codes(EAQECCs)play an important role in quantum communications with noise.Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum chan...Entanglement-assisted quantum error correction codes(EAQECCs)play an important role in quantum communications with noise.Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum channels by consuming some ebits between the sender(Alice)and the receiver(Bob).It is usually assumed that the preshared ebits of Bob are error free.However,noise on these ebits is unavoidable in many cases.In this work,we evaluate the performance of EAQECCs with noisy ebits over asymmetric quantum channels and quantum channels with memory by computing the exact entanglement fidelity of several EAQECCs.We consider asymmetric errors in both qubits and ebits and show that the performance of EAQECCs in entanglement fidelity gets improved for qubits and ebits over asymmetric channels.In quantum memory channels,we compute the entanglement fidelity of several EAQECCs over Markovian quantum memory channels and show that the performance of EAQECCs is lowered down by the channel memory.Furthermore,we show that the performance of EAQECCs is diverse when the error probabilities of qubits and ebits are different.In both asymmetric and memory quantum channels,we show that the performance of EAQECCs is improved largely when the error probability of ebits is reasonably smaller than that of qubits.展开更多
The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the co...The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.展开更多
A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check(QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Ur...A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check(QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke(RU) algorithm. Furthermore, a novel irregular QC-LDPC(4 288, 4 020) code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain(NCG) of the novel irregular QC-LDPC(4 288,4 020) code is respectively 2.08 d B, 1.25 d B and 0.29 d B more than those of the classic RS(255, 239) code, the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code at the bit error rate(BER) of 10^(-6). The irregular QC-LDPC(4 288, 4 020) code has the lower encoding/decoding complexity compared with the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code. The proposed novel QC-LDPC(4 288, 4 020) code can be more suitable for the increasing development requirements of high-speed optical transmission systems.展开更多
Along with the proliferating research interest in semantic communication(Sem Com),joint source channel coding(JSCC)has dominated the attention due to the widely assumed existence in efficiently delivering information ...Along with the proliferating research interest in semantic communication(Sem Com),joint source channel coding(JSCC)has dominated the attention due to the widely assumed existence in efficiently delivering information semantics.Nevertheless,this paper challenges the conventional JSCC paradigm and advocates for adopting separate source channel coding(SSCC)to enjoy a more underlying degree of freedom for optimization.We demonstrate that SSCC,after leveraging the strengths of the Large Language Model(LLM)for source coding and Error Correction Code Transformer(ECCT)complemented for channel coding,offers superior performance over JSCC.Our proposed framework also effectively highlights the compatibility challenges between Sem Com approaches and digital communication systems,particularly concerning the resource costs associated with the transmission of high-precision floating point numbers.Through comprehensive evaluations,we establish that assisted by LLM-based compression and ECCT-enhanced error correction,SSCC remains a viable and effective solution for modern communication systems.In other words,separate source channel coding is still what we need.展开更多
The main results in this paper are to construct two classes of plateaued functions with desirable cryptographic properties. By using the Maiorana-McFarland construction, a class of highly nonlinear resilient plateaued...The main results in this paper are to construct two classes of plateaued functions with desirable cryptographic properties. By using the Maiorana-McFarland construction, a class of highly nonlinear resilient plateaued functions satisfying the propagation criterion has been obtained. Johansson,s et al＇ s construction is modified slightly to obtain highly nonlinear multi-output resilient plateaued functions.展开更多
This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has sph...This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has spherical symmetry about the state of interest. The theoretical definition is given, as well the numerical approximation for practical purposes. The index is tested in some simple examples and the geometric distortion of the propagated error is studied for an inaccurate Shor 9-qubits correcting code.展开更多
Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construc...Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning(RL).By establishing reward and devising well-reasoned mappings from actions to states,it aims to facilitate the successful synthesis of binary or ternary LCD codes.Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies.The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds.Finally,it showcases how random network distillation aids agents in exploring beyond local optima,enhancing the overall performance of the models without compromising convergence.展开更多
A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encode...A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.展开更多
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Turbo code has drawn more and more attractions for high data rate transmission these years especially in W CDMA and CDMA2000 of the third generation mobile communications systems. In this paper, the simulation performance of turbo code under Rayleigh fading channel and additive white Gaussian channels are depicted. Comparison with the performance of convolutional code are made respect to different parameters, such as pilot length, interleaver size, frame length, mobile velocity and data rate, etc. Faithful results are drawn out.
基金Supported by National Natural Science Foundation of China under Grant No.69896246
文摘A new method to recover packet losses using (2,1,m) convolutional codes is proposed. The erasure correcting decoding algorithm and the decoding determinant theorem is presented. It is also proved that the codes with optimal distance profile have also optimal delay characteristic. Simulation results show that the proposed method can recover the packet losses more elliciently than RS codes over different decoding delay conditions and thus suits for different packet network delav conditions.
文摘The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.
文摘In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.
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.
文摘In the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting errors of the channel A is presented.
基金supported by the National Natural Science Foundation of China(No.61571072)the Basic and Advanced Technology Research Project in Chongqing(No.cstc2015jcyjA 40015)
文摘In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate(BER) is 10-6, in the same simulation environment, the net coding gain(NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.
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 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Project supported by the National Key R&D Program of China (Grant No.2022YFB3103802)the National Natural Science Foundation of China (Grant Nos.62371240 and 61802175)the Fundamental Research Funds for the Central Universities (Grant No.30923011014)。
文摘Entanglement-assisted quantum error correction codes(EAQECCs)play an important role in quantum communications with noise.Such a scheme can use arbitrary classical linear code to transmit qubits over noisy quantum channels by consuming some ebits between the sender(Alice)and the receiver(Bob).It is usually assumed that the preshared ebits of Bob are error free.However,noise on these ebits is unavoidable in many cases.In this work,we evaluate the performance of EAQECCs with noisy ebits over asymmetric quantum channels and quantum channels with memory by computing the exact entanglement fidelity of several EAQECCs.We consider asymmetric errors in both qubits and ebits and show that the performance of EAQECCs in entanglement fidelity gets improved for qubits and ebits over asymmetric channels.In quantum memory channels,we compute the entanglement fidelity of several EAQECCs over Markovian quantum memory channels and show that the performance of EAQECCs is lowered down by the channel memory.Furthermore,we show that the performance of EAQECCs is diverse when the error probabilities of qubits and ebits are different.In both asymmetric and memory quantum channels,we show that the performance of EAQECCs is improved largely when the error probability of ebits is reasonably smaller than that of qubits.
基金The authors extend their gratitude to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under grant number R.G.P.1/85/42.
文摘The decoding algorithm for the correction of errors of arbitrary Mannheim weight has discussed for Lattice constellations and codes from quadratic number fields.Following these lines,the decoding algorithms for the correction of errors of n=p−12 length cyclic codes(C)over quaternion integers of Quaternion Mannheim(QM)weight one up to two coordinates have considered.In continuation,the case of cyclic codes of lengths n=p−12 and 2n−1=p−2 has studied to improve the error correction efficiency.In this study,we present the decoding of cyclic codes of length n=ϕ(p)=p−1 and length 2n−1=2ϕ(p)−1=2p−3(where p is prime integer andϕis Euler phi function)over Hamilton Quaternion integers of Quaternion Mannheim weight for the correction of errors.Furthermore,the error correction capability and code rate tradeoff of these codes are also discussed.Thus,an increase in the length of the cyclic code is achieved along with its better code rate and an adequate error correction capability.
基金supported by the National Natural Science Foundation of China(Nos.61472464 and 61471075)the Program for Innovation Team Building at Institutions of Higher Education in Chongqing(No.J2013-46)+1 种基金the Natural Science Foundation of Chongqing Science and Technology Commission(Nos.cstc2015jcyjA 0554 and cstc2013jcyjA 40017)the Program for Postgraduate Science Research and Innovation of Chongqing University of Posts and Telecommunications(Chongqing Municipal Education Commission)(No.CYS14144)
文摘A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check(QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke(RU) algorithm. Furthermore, a novel irregular QC-LDPC(4 288, 4 020) code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain(NCG) of the novel irregular QC-LDPC(4 288,4 020) code is respectively 2.08 d B, 1.25 d B and 0.29 d B more than those of the classic RS(255, 239) code, the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code at the bit error rate(BER) of 10^(-6). The irregular QC-LDPC(4 288, 4 020) code has the lower encoding/decoding complexity compared with the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code. The proposed novel QC-LDPC(4 288, 4 020) code can be more suitable for the increasing development requirements of high-speed optical transmission systems.
基金supported in part by the National Key Research and Development Program of China under Grant No.2024YFE0200600the Zhejiang Provincial Natural Science Foundation of China under Grant No.LR23F010005the Huawei Cooperation Project under Grant No.TC20240829036。
文摘Along with the proliferating research interest in semantic communication(Sem Com),joint source channel coding(JSCC)has dominated the attention due to the widely assumed existence in efficiently delivering information semantics.Nevertheless,this paper challenges the conventional JSCC paradigm and advocates for adopting separate source channel coding(SSCC)to enjoy a more underlying degree of freedom for optimization.We demonstrate that SSCC,after leveraging the strengths of the Large Language Model(LLM)for source coding and Error Correction Code Transformer(ECCT)complemented for channel coding,offers superior performance over JSCC.Our proposed framework also effectively highlights the compatibility challenges between Sem Com approaches and digital communication systems,particularly concerning the resource costs associated with the transmission of high-precision floating point numbers.Through comprehensive evaluations,we establish that assisted by LLM-based compression and ECCT-enhanced error correction,SSCC remains a viable and effective solution for modern communication systems.In other words,separate source channel coding is still what we need.
基金Supported by the National Natural Science Foundations of China （No. 60773003, 60970120, 60903180）, the Natural Science Basic Research Plan in Shanx/Province of China （No. S JOB -ZTI4 ）, and the Fundamental Research Funds For the Central Universities and the 111 Project （ No. B08038 ）.
文摘The main results in this paper are to construct two classes of plateaued functions with desirable cryptographic properties. By using the Maiorana-McFarland construction, a class of highly nonlinear resilient plateaued functions satisfying the propagation criterion has been obtained. Johansson,s et al＇ s construction is modified slightly to obtain highly nonlinear multi-output resilient plateaued functions.
文摘This article describes a proposal for a double index to estimate the isotropic components of unitary errors in a quantum computation circuit. In the context of this work the error is considered isotropic if it has spherical symmetry about the state of interest. The theoretical definition is given, as well the numerical approximation for practical purposes. The index is tested in some simple examples and the geometric distortion of the propagated error is studied for an inaccurate Shor 9-qubits correcting code.
基金supported by the National Natural Science Foundation of China under Grant Nos.62372247 and 12441103the open research fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2025D01the Open Project of Guangxi Provincial Key Laboratory under Grant No.MIMS22-01。
文摘Recently,linear complementary dual(LCD)codes have garnered substantial interest within coding theory research due to their diverse applications and favorable attributes.This paper directs its attention to the construction of binary and ternary LCD codes leveraging curiosity-driven reinforcement learning(RL).By establishing reward and devising well-reasoned mappings from actions to states,it aims to facilitate the successful synthesis of binary or ternary LCD codes.Experimental results indicate that LCD codes constructed using RL exhibit slightly superior error-correction performance compared to those conventionally constructed LCD codes and those developed via standard RL methodologies.The paper introduces novel binary and ternary LCD codes with enhanced minimum distance bounds.Finally,it showcases how random network distillation aids agents in exploring beyond local optima,enhancing the overall performance of the models without compromising convergence.
基金supported in part by National Natural Science Foundation of China under Grant Nos.60573127,60773012,and 60873082Natural Science Foundation of Hunan Province under Grant Nos.07JJ3128 and 2008RS4016+1 种基金Scientific Research Fund of Hunan Provincial Education Department under Grant No.08B011Postdoctoral Science Foundation of China under Grant Nos.20070420184 and 200801341
文摘A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.
