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
In mobile computing environments, most IoT devices connected to networks experience variable error rates and possess limited bandwidth. The conventional method of retransmitting lost information during transmission, c...In mobile computing environments, most IoT devices connected to networks experience variable error rates and possess limited bandwidth. The conventional method of retransmitting lost information during transmission, commonly used in data transmission protocols, increases transmission delay and consumes excessive bandwidth. To overcome this issue, forward error correction techniques, e.g., Random Linear Network Coding(RLNC) can be used in data transmission. The primary challenge in RLNC-based methodologies is sustaining a consistent coding ratio during data transmission, leading to notable bandwidth usage and transmission delay in dynamic network conditions. Therefore, this study proposes a new block-based RLNC strategy known as Adjustable RLNC(ARLNC), which dynamically adjusts the coding ratio and transmission window during runtime based on the estimated network error rate calculated via receiver feedback. The calculations in this approach are performed using a Galois field with the order of 256. Furthermore, we assessed ARLNC's performance by subjecting it to various error models such as Gilbert Elliott, exponential, and constant rates and compared it with the standard RLNC. The results show that dynamically adjusting the coding ratio and transmission window size based on network conditions significantly enhances network throughput and reduces total transmission delay in most scenarios. In contrast to the conventional RLNC method employing a fixed coding ratio, the presented approach has demonstrated significant enhancements, resulting in a 73% decrease in transmission delay and a 4 times augmentation in throughput. However, in dynamic computational environments, ARLNC generally incurs higher computational costs than the standard RLNC but excels in high-performance networks.展开更多
Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long bee...Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.展开更多
Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,...Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.展开更多
This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block co...This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.展开更多
To adjust the variance of source rate in linear broadcast networks, global encoding kernels should have corresponding dimensions to instruct the decoding process. The algorithm of constructing such global encoding ker...To adjust the variance of source rate in linear broadcast networks, global encoding kernels should have corresponding dimensions to instruct the decoding process. The algorithm of constructing such global encoding kernels is to adjust heterogeneous network to possible link failures. Linear algebra, graph theory and group theory are applied to construct one series of global encoding kernels which are applicable to all source rates. The effectiveness and existence of such global encoding kernels are proved. Based on 2 information flow, the algorithm of construction is explicitly given within polynomial time O（｜E｜ ｜T｜.ω^2max）, and the memory complexity of algorithm is O（｜E｜）. Both time and memory complexity of this algorithm proposed can be O（ωmax） less than those of algorithms in related works.展开更多
In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenar...In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenario where the demands of a vehicle are satisfied by cooperative transmissions from those one in front is considered.Since the topology of the vehicle network is dynamic,random linear network coding is applied in such a multisource single-sink vehicle-to-vehicle network,where each vehicle is assumed to broadcast messages to others so that the intermediate vehicles between sources and sink can reduce the latency collaboratively.It is shown that the coding scheme can significantly reduce the time delay compared with the non-coding scheme even in the channels with high packet loss rate.In order to further optimize the coding scheme,one can increase the generation size,where the generation size means the number of raw data packets sent by the source node to the sink node in each round of communication.Under the premise of satisfying the coding validity,we can dynamically select the Galois field size according to the number of intermediate nodes.It is not surprised that the reduction in the Galois field size can further reduce the transmission latency.展开更多
Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding proc...Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.展开更多
Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/...Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.展开更多
The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matr...The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.展开更多
The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructe...The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n,n + 2k, ≥min(8, n,2d)) linear codes are resulted from quaternary (n,k,d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.展开更多
Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum di...Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum distance of cyclic codes is analyzed via linear complexityof sequences,and new theorems about the lower bounds are obtained.展开更多
A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC...A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.展开更多
Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in ...Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a （all） sink（s） represents the impact of major parameters, i.e., the size of field, the number of relays （and sinks） and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers＇ capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.展开更多
In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we part...In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.展开更多
A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify h...A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid share.Another does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.展开更多
In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric ...In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.展开更多
m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking ...m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.展开更多
We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several m...We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-展开更多
Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memor...Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.展开更多
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.
文摘In mobile computing environments, most IoT devices connected to networks experience variable error rates and possess limited bandwidth. The conventional method of retransmitting lost information during transmission, commonly used in data transmission protocols, increases transmission delay and consumes excessive bandwidth. To overcome this issue, forward error correction techniques, e.g., Random Linear Network Coding(RLNC) can be used in data transmission. The primary challenge in RLNC-based methodologies is sustaining a consistent coding ratio during data transmission, leading to notable bandwidth usage and transmission delay in dynamic network conditions. Therefore, this study proposes a new block-based RLNC strategy known as Adjustable RLNC(ARLNC), which dynamically adjusts the coding ratio and transmission window during runtime based on the estimated network error rate calculated via receiver feedback. The calculations in this approach are performed using a Galois field with the order of 256. Furthermore, we assessed ARLNC's performance by subjecting it to various error models such as Gilbert Elliott, exponential, and constant rates and compared it with the standard RLNC. The results show that dynamically adjusting the coding ratio and transmission window size based on network conditions significantly enhances network throughput and reduces total transmission delay in most scenarios. In contrast to the conventional RLNC method employing a fixed coding ratio, the presented approach has demonstrated significant enhancements, resulting in a 73% decrease in transmission delay and a 4 times augmentation in throughput. However, in dynamic computational environments, ARLNC generally incurs higher computational costs than the standard RLNC but excels in high-performance networks.
基金supported by China Postdoctoral Science Foundation(No.2020M670469)National Key Research and Development Program of China(No.2019YFB1803303,No.2020YFB1806702).
文摘Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.
文摘Linear dispersion codes (LDCs) were originally designed based on maximum likelihood detection. They do not have good performance when using ordered successive interference cancellation (OSIC) detection. In this paper,we propose a new improved linear dispersion codes transmission scheme to combat performance loss of original LDCs when using OSIC detection. We introduce an interleaver to each data substream transmitted over different antennas after LDCs encoder. Furthermore,a new computer search criterion for a linear transformation matrix is also proposed. New search criterion is to minimize the symbol error rate based on OSIC detection. Computer simulations show that the performance of proposed LDCs transmission scheme is better than the original LDCs.
基金supported by the National Natural Science Foundation of China(61171170) the Natural Science Foundation of Anhui Province(1408085QF115)
文摘This study proposes a novel multi-fractal spectrumbasedapproach to distinguish linear block codes from its selfsynchronousscrambled codes. Given that the linear block codeand self-synchronous scrambled linear block code share the propertyof linear correlation, the existing linear correlation-basedidentification method is invalid for this case. This drawback can becircumvented by introducing a novel multi-fractal spectrum-basedmethod. Simulation results show that the new method has highrobustness and under the same conditions of bit error, the lowerthe code rate, the higher the recognition rate. Thus, the methodhas significant potential for future application in engineering.
基金Project(60872005) supported by National Natural Science Foundation of China
文摘To adjust the variance of source rate in linear broadcast networks, global encoding kernels should have corresponding dimensions to instruct the decoding process. The algorithm of constructing such global encoding kernels is to adjust heterogeneous network to possible link failures. Linear algebra, graph theory and group theory are applied to construct one series of global encoding kernels which are applicable to all source rates. The effectiveness and existence of such global encoding kernels are proved. Based on 2 information flow, the algorithm of construction is explicitly given within polynomial time O（｜E｜ ｜T｜.ω^2max）, and the memory complexity of algorithm is O（｜E｜）. Both time and memory complexity of this algorithm proposed can be O（ωmax） less than those of algorithms in related works.
基金This work was supported in part by the Guangdong Basic and Applied Basic Research Foundation under Key Project 2019B1515120032in part by the National Science Foundation of China(NSFC)with grant no.61901534+3 种基金in part by the Science,Technology and Innovation Commission of Shenzhen Municipality with grant no.JCYJ20190807155617099in part by the University Basic Research Fund 20lgpy43in part by the Guangdong Natural Science Foundation of Grant No.2019A1515011622the Foundation of Grant No.2019-JCJQ-JJ-411.
文摘In the Internet of vehicles(IoV),direct communication between vehicles,i.e.,vehicle-tovehicle(V2V)may have lower latency,compared to the schemes with help of Road Side Unit(RSU)or base station.In this paper,the scenario where the demands of a vehicle are satisfied by cooperative transmissions from those one in front is considered.Since the topology of the vehicle network is dynamic,random linear network coding is applied in such a multisource single-sink vehicle-to-vehicle network,where each vehicle is assumed to broadcast messages to others so that the intermediate vehicles between sources and sink can reduce the latency collaboratively.It is shown that the coding scheme can significantly reduce the time delay compared with the non-coding scheme even in the channels with high packet loss rate.In order to further optimize the coding scheme,one can increase the generation size,where the generation size means the number of raw data packets sent by the source node to the sink node in each round of communication.Under the premise of satisfying the coding validity,we can dynamically select the Galois field size according to the number of intermediate nodes.It is not surprised that the reduction in the Galois field size can further reduce the transmission latency.
基金She was with the Department of Mathematics in Wuhan University while writting this paper.
文摘Abraham Lempel et al made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique.
文摘Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.
文摘The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented.The minimum distance and weight property lemmas and the theorem are proved for the generator matrix.Based upon the property of generator matrix,the structured algorithms of linear block codes are demonstrated.Since the complexity of optimal structured algorithm is very high,the binary linear block codes is searched by using the suboptimal structured algorithm.The comparison with Bose-Chaudhuri-Hocquenqhem（BCH） codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths.Because the linear block codes are used widely in communication systems and digital applications,the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.
文摘The binary extended Golay code has a two-level structure, which can be used in the decoding of the code. However, such structure is not limited to the Golay code, in fact, several binary linear codes can be constructed by a projective method which is related to the structure. In this correspondence, the binary (4n,n + 2k, ≥min(8, n,2d)) linear codes are resulted from quaternary (n,k,d) linear block codes. Based on the structure, the efficient maximum likelihood decoding algorithms can be presented correspondingly for the derived codes.
文摘Firstly,the Fourier transforms in finite fields and the concept of linear complexityof sequences are described.Then several known lower bounds on the minimum distance of cycliccodes are outlined.Finally,the minimum distance of cyclic codes is analyzed via linear complexityof sequences,and new theorems about the lower bounds are obtained.
基金Sponsored by the "111" Project of China (B08038)Important National Science & Technology Specific Projects (2009ZX03003-003+2 种基金2009ZX03003-004) the NSFC-Guangdong (U0635003)Program for Changjiang Scholars and Innovative Research Team in University(IRT0852)
文摘A new architecture of space-time codes as a combination of orthogonal space-time block codes （OSTBC） and linear dispersion codes （LDC） is proposed in order to improve the bit error rate（BER） performance of OSTBC.The scheme proposed is named linear dispersion orthogonal space-time block codes （LDOSTBC）.In LDOSTBC scheme,firstly,the data is coded into LDC codewords.Then,the coded LDC substreams are coded into OSTBC codewords again.The decoding algorithm of LDOSTBC combines linear decoding of OSTBC and ML decoding or suboptimum detection algorithms of LDC.Compared with OSTBC scheme when the rate of LDC is MtR,the performance of LDOSTBC scheme can be improved without decreasing the data rate,where Mt is the number of transmit antennas and R is the spectral efficiency of the modulation constellation.If some rate penalty is allowed,when the rate of LDC is less than MtR the performance of LDOSTBC can be improved further.
基金Supported by the National Natural Science Foundation of China(61271174,61301178)the Science and Technology Innovation Foundation of Xi’an(CXY1352WL28)
文摘Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a （all） sink（s） represents the impact of major parameters, i.e., the size of field, the number of relays （and sinks） and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers＇ capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.
基金Supported by the National Natural Science Foundation of China (11271237)
文摘In this paper, we propose a novel space efficient secret sharing scheme on the basis of minimal linear codes, which satisfies the definition of a computationally efficient secret sharing scheme. In the scheme, we partition the underlying minimal linear code into disjoint classes, establishing a one-to-one correspondence between the minimal authorized subsets of participants and the representative codewords of all different classes. Each participant, with only one short share transmitted through a public channel, can share a large secret. Therefore, the proposed scheme can distribute a large secret in practical applications such as secure information dispersal in sensor networks and secure multiparty computation.
文摘A secret sharing system can be damaged when the dealer cheating occurs.In this paper,two kinds of secret sharing schemes based on linear code are proposed.One is a verifiable scheme which each participant can verify his own share from dealer's distribution and ensure each participant to receive valid share.Another does not have a trusted center,here,each participant plays a dual-role as the dealer and shadow(or share) provider in the whole scheme.
基金Supported by the Scientific Research Foundation of Hubei Provincial Education Department of China(Q20174503)the National Science Foundation of Hubei Polytechnic University of China(12xjz14A and 17xjz03A)。
文摘In this paper,we first give the definition of the Euclidean sums of linear codes,and prove that the Euclidean sums of linear codes are Euclidean dual-containing.Then we construct two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of the Reed-Solomon codes,and two new classes of optimal asymmetric quantum error-correcting codes based on Euclidean sums of linear codes generated by Vandermonde matrices over finite fields.Moreover,these optimal asymmetric quantum errorcorrecting codes constructed in this paper are different from the ones in the literature.
基金Supported by the National Program on Basic Sciences(973 Program,G19990751Q2)
文摘m-weight,as a new generalization of classical Hamming weight,was discussedin this paper.A condition for the existence of linear codes of certain m-weights was given;theSingleton bound,Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.
文摘We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-
文摘Genetic algorithms offer very good performances for solving large optimization problems, especially in the domain of error-correcting codes. However, they have a major drawback related to the time complexity and memory occupation when running on a uniprocessor computer. This paper proposes a parallel decoder for linear block codes, using parallel genetic algorithms (PGA). The good performance and time complexity are confirmed by theoretical study and by simulations on BCH(63,30,14) codes over both AWGN and flat Rayleigh fading channels. The simulation results show that the coding gain between parallel and single genetic algorithm is about 0.7 dB at BER = 10﹣5 with only 4 processors.
