In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over ...In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).展开更多
Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to...Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.展开更多
The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel c...The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.展开更多
Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbule...Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbulence intensities,the deep learning technique is proposed to the polarization code decoding in ACO-OFDM space optical communication system.Moreover,this system realizes the polarization code decoding and signal demodulation without frequency conduction with superior performance and robustness compared with the performance of traditional decoder.Simulations under different turbulence intensities as well as different mapping orders show that the convolutional neural network(CNN)decoder trained under weak-medium-strong turbulence atmospheric channels achieves a performance improvement of about 10^(2)compared to the conventional decoder at 4-quadrature amplitude modulation(4QAM),and the BERs for both 16QAM and 64QAM are in between those of the conventional decoder.展开更多
The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction perform...The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction performance of channel coding functions as a significant way of optimizing the transmission reliability and efficiency.In this paper,the efficient estimation methods of the block error rate(BLER)performance for rate-compatible polar codes(RCPC)are proposed under several scenarios.Firstly,the BLER performance of RCPC is generally evaluated in the additive white Gaussian noise channels.That is further extended into the Rayleigh fading channel case using an equivalent estimation method.Moreover,with respect to the powerful decoder such as successive cancellation list decoding,the performance estimation is derived analytically based on the polar weight spectrum and BLER upper bounds.Theoretical evaluation and numerical simulation results show that the estimated performance can fit well the practical simulated results of RCPC under the objective conditions,verifying the validity of our proposed performance estimation methods.Furthermore,the application designs of the reliability estimation of RCPC are explored,particularly in the advantages of the signal-to-noise(SNR)estimation and throughput efficiency optimization of polar coded hybrid automatic repeat request.展开更多
Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementa...Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementation of low-density paritycheck(LDPC)decoding under resource-restricted space platforms.Particularly,due to the supply restriction and cost issues of high-speed on-board devices such as analog-to-digital converters(ADCs),the input of LDPC decoding will be usually constrained by hard-decision channel output.To tackle this challenge,density-evolution-based theoretical analysis is firstly performed to identify the cause of performance degradation in the conventional binaryinitialized iterative decoding(BIID)algorithm.Then,a computation-efficient decoding algorithm named multiary-initialized iterative decoding with early termination(MIID-ET)is proposed,which improves the error-correcting performance and computation efficiency by using a reliability-based initialization method and a threshold-based decoding termination rule.Finally,numerical simulations are conducted on example codes of rates 7/8 and 1/2 to evaluate the performance of different LDPC decoding algorithms,where the proposed MIID-ET outperforms the BIID with a coding gain of 0.38 dB and variable node calculation saving of 37%.With this advantage,the proposed MIID-ET can notably reduce LDPC decoder’s hardware implementation complexity under the same bit error rate performance,which successfully doubles the total throughput to 10 Gbps on a single-chip FPGA.展开更多
Digital content such as games,extended reality(XR),and movies has been widely and easily distributed over wireless networks.As a result,unauthorized access,copyright infringement by third parties or eavesdroppers,and ...Digital content such as games,extended reality(XR),and movies has been widely and easily distributed over wireless networks.As a result,unauthorized access,copyright infringement by third parties or eavesdroppers,and cyberattacks over these networks have become pressing concerns.Therefore,protecting copyrighted content and preventing illegal distribution in wireless communications has garnered significant attention.The Intelligent Reflecting Surface(IRS)is regarded as a promising technology for future wireless and mobile networks due to its ability to reconfigure the radio propagation environment.This study investigates the security performance of an uplink Non-Orthogonal Multiple Access(NOMA)system integrated with an IRS and employing Fountain Codes(FCs).Specifically,two users send signals to the base station at separate distances.A relay receives the signal from the nearby user first and then relays it to the base station.The IRS receives the signal from the distant user and reflects it to the relay,which then sends the reflected signal to the base station.Furthermore,a malevolent eavesdropper intercepts both user and relay communications.We construct mathematical equations for Outage Probability(OP),throughput,diversity evaluation,and Interception Probability(IP),offering quantitative insights to assess system security and performance.Additionally,OP and IP are analyzed using a Deep Neural Network(DNN)model.A deeper comprehension of the security performance of the IRS-assisted NOMA systemin signal transmission is provided by Monte Carlo simulations,which are also carried out to confirm the theoretical conclusions.展开更多
Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub&g...Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.展开更多
Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into...Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.展开更多
This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and...This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated,respectively.The genetic algorithm is then utilized to optimize the base matrices and the replacement ones.The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and Bei Dou satellite navigation system.展开更多
In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the e...In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.展开更多
The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity comm...The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity communication systems,an integrated framework has been established to analyze the theoretical error performance of polar codes in correlated block fading channels.First,the upper bound on error probabil-ity of polarized channels is derived based on split po-lar spectrum,which is fully determined by covariance channel matrix as well as the block-wise weight distri-bution of the corresponding polar subcode.Further,to facilitate practical implementations,we design a con-struction metric named polarized correlation weight(PCW)to generate polar codes in correlated block fad-ing channels.Finally,simulation results on block error rate indicate that the proposed metric can exhibit both diversity gain and coding gain compared to the con-ventional methods under successive cancellation de-coding.展开更多
Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-med...Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-medium length regime.However,this list decoding complexity becomes formidable as the decoding output list size increases.This is primarily incurred by the OSD.Addressing this challenge,this paper proposes the low complexity SCL decoding through reducing the complexity of component code decoding,and pruning the redundant SCL decoding paths.For the former,an efficient skipping rule is introduced for the OSD so that the higher order decoding can be skipped when they are not possible to provide a more likely codeword candidate.It is further extended to the OSD variant,the box-andmatch algorithm(BMA),in facilitating the component code decoding.Moreover,through estimating the correlation distance lower bounds(CDLBs)of the component code decoding outputs,a path pruning(PP)-SCL decoding is proposed to further facilitate the decoding of U-UV codes.In particular,its integration with the improved OSD and BMA is discussed.Simulation results show that significant complexity reduction can be achieved.Consequently,the U-UV codes can outperform the cyclic redundancy check(CRC)-polar codes with a similar decoding complexity.展开更多
The progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance ...The progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance of LDPC codes,many im-proved PEG(IPEG)algorithms employ multi metrics to select surviving edges in turn.In this paper,the pro-posed edges metric(EM)based on message-passing algorithm(MPA)is introduced to PEG algorithm and the proposed EM constrained PEG(EM-PEG)algo-rithm mainly considers the independence of message passing from different nodes in Tanner graph.The numerical results show that our EM-PEG algorithm brings better bit error rate(BER)performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm(MM-PEGA)proposed recently.In ad-dition,the multi-edge EM constrained PEG(M-EM-PEG)algorithm which adopts multi-edge EM may fur-ther improve the BER performance.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
Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first...Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.展开更多
Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rat...Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.展开更多
In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese...In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.展开更多
In relay-assisted multi-user system, relay coding is important to enhance the robustness and reliability of cooperative transmission. For better adaptability and efficiency, two joint network and fountain coding(JNFC)...In relay-assisted multi-user system, relay coding is important to enhance the robustness and reliability of cooperative transmission. For better adaptability and efficiency, two joint network and fountain coding(JNFC) schemes are proposed. When the condition of all direct channels is worse, JNFC scheme based on distributed LT(DLT) codes is used. Otherwise, JNFC scheme based on multi-dimensional LT(MD-LT) codes is suited. For both two above-mentioned schemes, the united degree distribution design method for short-length fountain codes is proposed. For the latter scheme, MD-LT codes are proposed for equal error protection(EEP) of each user. Simulation results and analysis show that the united degree distribution need less decoding overhead compared with other degree distribution for short-length fountain codes. And then, all users are protected equally in despite of asymmetric uplinks.展开更多
Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulti...Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.展开更多
基金Supported by Research Funds of Hubei Province(D20144401,Q20174503)。
文摘In this paper,we first generalize the constant dimension and orbit codes over finite fields to the constant rank and orbit codes over finite chain rings.Then we provide a relationship between constant rank codes over finite chain rings and constant dimension codes over the residue fields.In particular,we prove that an orbit submodule code over a finite chain ring is a constant rank code.Finally,for special finite chain ring F_(q)+γF_(q),we define a Gray mapφfrom(F_(q)+γF_(q))^(n)to F^(2n)_(q),and by using cyclic codes over F_(q)+γF_(q),we obtain a method of constructing an optimum distance constant dimension code over F_(q).
文摘Let m ≥ 2 be any natural number and let be a finite non-chain ring, where and q is a prime power congruent to 1 modulo (m-1). In this paper we study duadic codes over the ring and their extensions. A Gray map from to is defined which preserves self duality of linear codes. As a consequence self-dual, formally self-dual and self-orthogonal codes over are constructed. Some examples are also given to illustrate this.
基金Supported by the National Natural Science Foundation ofChina (No. 61071145,41074090)the Specialized Research Fund for the Doctoral Program of Higher Education (200802880014)
文摘The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.
基金supported by the National Natural Science Foundation of China(No.12104141).
文摘Aiming at the problem that the bit error rate(BER)of asymmetrically clipped optical orthogonal frequency division multiplexing(ACO-OFDM)space optical communication system is significantly affected by different turbulence intensities,the deep learning technique is proposed to the polarization code decoding in ACO-OFDM space optical communication system.Moreover,this system realizes the polarization code decoding and signal demodulation without frequency conduction with superior performance and robustness compared with the performance of traditional decoder.Simulations under different turbulence intensities as well as different mapping orders show that the convolutional neural network(CNN)decoder trained under weak-medium-strong turbulence atmospheric channels achieves a performance improvement of about 10^(2)compared to the conventional decoder at 4-quadrature amplitude modulation(4QAM),and the BERs for both 16QAM and 64QAM are in between those of the conventional decoder.
基金supported by National Natural Science Foundation of China(No.62201596)Research Planning Project of National University of Defense Technology(ZK22-45).
文摘The beyond fifth-generation Internet of Things requires more capable channel coding schemes to achieve high-reliability,low-complexity and lowlatency communications.The theoretical analysis of error-correction performance of channel coding functions as a significant way of optimizing the transmission reliability and efficiency.In this paper,the efficient estimation methods of the block error rate(BLER)performance for rate-compatible polar codes(RCPC)are proposed under several scenarios.Firstly,the BLER performance of RCPC is generally evaluated in the additive white Gaussian noise channels.That is further extended into the Rayleigh fading channel case using an equivalent estimation method.Moreover,with respect to the powerful decoder such as successive cancellation list decoding,the performance estimation is derived analytically based on the polar weight spectrum and BLER upper bounds.Theoretical evaluation and numerical simulation results show that the estimated performance can fit well the practical simulated results of RCPC under the objective conditions,verifying the validity of our proposed performance estimation methods.Furthermore,the application designs of the reliability estimation of RCPC are explored,particularly in the advantages of the signal-to-noise(SNR)estimation and throughput efficiency optimization of polar coded hybrid automatic repeat request.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1005000)the National Natural Science Foundation of China(Grant No.62101308 and 62025110).
文摘Space laser communication(SLC)is an emerging technology to support high-throughput data transmissions in space networks.In this paper,to guarantee the reliability of high-speed SLC links,we aim at practical implementation of low-density paritycheck(LDPC)decoding under resource-restricted space platforms.Particularly,due to the supply restriction and cost issues of high-speed on-board devices such as analog-to-digital converters(ADCs),the input of LDPC decoding will be usually constrained by hard-decision channel output.To tackle this challenge,density-evolution-based theoretical analysis is firstly performed to identify the cause of performance degradation in the conventional binaryinitialized iterative decoding(BIID)algorithm.Then,a computation-efficient decoding algorithm named multiary-initialized iterative decoding with early termination(MIID-ET)is proposed,which improves the error-correcting performance and computation efficiency by using a reliability-based initialization method and a threshold-based decoding termination rule.Finally,numerical simulations are conducted on example codes of rates 7/8 and 1/2 to evaluate the performance of different LDPC decoding algorithms,where the proposed MIID-ET outperforms the BIID with a coding gain of 0.38 dB and variable node calculation saving of 37%.With this advantage,the proposed MIID-ET can notably reduce LDPC decoder’s hardware implementation complexity under the same bit error rate performance,which successfully doubles the total throughput to 10 Gbps on a single-chip FPGA.
基金supported in part by Vietnam National Foundation for Science and Technology Development(NAFOSTED)under Grant 102.04-2021.57in part by Culture,Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture,Sports and Tourism in 2024(Project Name:Global Talent Training Program for Copyright Management Technology in Game Contents,Project Number:RS-2024-00396709,Contribution Rate:100%).
文摘Digital content such as games,extended reality(XR),and movies has been widely and easily distributed over wireless networks.As a result,unauthorized access,copyright infringement by third parties or eavesdroppers,and cyberattacks over these networks have become pressing concerns.Therefore,protecting copyrighted content and preventing illegal distribution in wireless communications has garnered significant attention.The Intelligent Reflecting Surface(IRS)is regarded as a promising technology for future wireless and mobile networks due to its ability to reconfigure the radio propagation environment.This study investigates the security performance of an uplink Non-Orthogonal Multiple Access(NOMA)system integrated with an IRS and employing Fountain Codes(FCs).Specifically,two users send signals to the base station at separate distances.A relay receives the signal from the nearby user first and then relays it to the base station.The IRS receives the signal from the distant user and reflects it to the relay,which then sends the reflected signal to the base station.Furthermore,a malevolent eavesdropper intercepts both user and relay communications.We construct mathematical equations for Outage Probability(OP),throughput,diversity evaluation,and Interception Probability(IP),offering quantitative insights to assess system security and performance.Additionally,OP and IP are analyzed using a Deep Neural Network(DNN)model.A deeper comprehension of the security performance of the IRS-assisted NOMA systemin signal transmission is provided by Monte Carlo simulations,which are also carried out to confirm the theoretical conclusions.
文摘Let <i>f</i>(u) and <i>g</i>(v) be two polynomials of degree <i>k</i> and <i>l</i> respectively, not both linear which split into distinct linear factors over F<sub>q</sub>. Let <img src="Edit_83041428-d8b0-4505-8c3c-5e29f2886159.png" width="160" height="15" alt="" /> be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring <i>R</i>. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from <img src="Edit_c75f119d-3176-4a71-a36a-354955044c09.png" width="50" height="15" alt="" /> which preserves duality. The Gray images of polyadic codes and their extensions over the ring <i>R</i> lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over F<i><sub>q</sub></i>. Some examples are also given to illustrate this.
文摘Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.
基金supported by the National Natural Science Foundation of China under Grants 62331002。
文摘This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check(NB-QC-LDPC)codes with short block lengths.In our scheme,the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated,respectively.The genetic algorithm is then utilized to optimize the base matrices and the replacement ones.The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and Bei Dou satellite navigation system.
文摘In this paper,a sparse graph neural network-aided(SGNN-aided)decoder is proposed for improving the decoding performance of polar codes under bursty interference.Firstly,a sparse factor graph is constructed using the encoding characteristic to achieve high-throughput polar decoding.To further improve the decoding performance,a residual gated bipartite graph neural network is designed for updating embedding vectors of heterogeneous nodes based on a bidirectional message passing neural network.This framework exploits gated recurrent units and residual blocks to address the gradient disappearance in deep graph recurrent neural networks.Finally,predictions are generated by feeding the embedding vectors into a readout module.Simulation results show that the proposed decoder is more robust than the existing ones in the presence of bursty interference and exhibits high universality.
基金supported by National Natural Science Foundation of China(No.62471054).
文摘The construction of polar codes in corre-lated block fading channels is still an open issue to be solved.In this paper,to explicitly reveal the impact of correlation on error performance of polar coded diver-sity communication systems,an integrated framework has been established to analyze the theoretical error performance of polar codes in correlated block fading channels.First,the upper bound on error probabil-ity of polarized channels is derived based on split po-lar spectrum,which is fully determined by covariance channel matrix as well as the block-wise weight distri-bution of the corresponding polar subcode.Further,to facilitate practical implementations,we design a con-struction metric named polarized correlation weight(PCW)to generate polar codes in correlated block fad-ing channels.Finally,simulation results on block error rate indicate that the proposed metric can exhibit both diversity gain and coding gain compared to the con-ventional methods under successive cancellation de-coding.
基金supported by the National Natural Science Foundation of China(NSFC)with project ID 62071498the Guangdong National Science Foundation(GDNSF)with project ID 2024A1515010213.
文摘Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-medium length regime.However,this list decoding complexity becomes formidable as the decoding output list size increases.This is primarily incurred by the OSD.Addressing this challenge,this paper proposes the low complexity SCL decoding through reducing the complexity of component code decoding,and pruning the redundant SCL decoding paths.For the former,an efficient skipping rule is introduced for the OSD so that the higher order decoding can be skipped when they are not possible to provide a more likely codeword candidate.It is further extended to the OSD variant,the box-andmatch algorithm(BMA),in facilitating the component code decoding.Moreover,through estimating the correlation distance lower bounds(CDLBs)of the component code decoding outputs,a path pruning(PP)-SCL decoding is proposed to further facilitate the decoding of U-UV codes.In particular,its integration with the improved OSD and BMA is discussed.Simulation results show that significant complexity reduction can be achieved.Consequently,the U-UV codes can outperform the cyclic redundancy check(CRC)-polar codes with a similar decoding complexity.
文摘The progressive edge-growth(PEG)al-gorithm is a general method to construct short low-density parity-check(LDPC)codes and it is a greedy method to place each edge with large girths.In order to improve the performance of LDPC codes,many im-proved PEG(IPEG)algorithms employ multi metrics to select surviving edges in turn.In this paper,the pro-posed edges metric(EM)based on message-passing algorithm(MPA)is introduced to PEG algorithm and the proposed EM constrained PEG(EM-PEG)algo-rithm mainly considers the independence of message passing from different nodes in Tanner graph.The numerical results show that our EM-PEG algorithm brings better bit error rate(BER)performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm(MM-PEGA)proposed recently.In ad-dition,the multi-edge EM constrained PEG(M-EM-PEG)algorithm which adopts multi-edge EM may fur-ther improve the BER performance.
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.
基金The National Key Technology R&D Program of China during the 12th Five-Year Plan Period(No.2012BAH15B00)
文摘Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.
基金This work was supported in part by National Natural Science Foundation of China(No.61671324)the Director’s Funding from Pilot National Laboratory for Marine Science and Technology(Qingdao)(QNLM201712).
文摘Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.
基金supported by the Natural ScienceFoundation of Hubei Province(D2014401)the Natural Science Foundation of Hubei Polytechnic University(12xjz14A)
文摘In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.
基金supported in part by a grant from the Ph.D. Programs Foundation of Ministry of Education of China under Grants No. 20094307110004National Natural Science Foundation of China under Grants No.61372098, No.61101074Natural Science Foundation of Hunan Province, China under Grants No.12jj2037
文摘In relay-assisted multi-user system, relay coding is important to enhance the robustness and reliability of cooperative transmission. For better adaptability and efficiency, two joint network and fountain coding(JNFC) schemes are proposed. When the condition of all direct channels is worse, JNFC scheme based on distributed LT(DLT) codes is used. Otherwise, JNFC scheme based on multi-dimensional LT(MD-LT) codes is suited. For both two above-mentioned schemes, the united degree distribution design method for short-length fountain codes is proposed. For the latter scheme, MD-LT codes are proposed for equal error protection(EEP) of each user. Simulation results and analysis show that the united degree distribution need less decoding overhead compared with other degree distribution for short-length fountain codes. And then, all users are protected equally in despite of asymmetric uplinks.
基金partially supported by the National Key Research and Development Project under Grant 2020YFB1806805。
文摘Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.
