Self-encoded spread spectrum eliminates the need for traditional pseudo noise (PN) code generators. In a self-encoded multiple access (SEMA) system, the number of users is not limited by the number of available sequen...Self-encoded spread spectrum eliminates the need for traditional pseudo noise (PN) code generators. In a self-encoded multiple access (SEMA) system, the number of users is not limited by the number of available sequences, unlike code division multiple access (CDMA) systems that employ PN codes such as m-, Gold or Kassami sequences. SEMA provides a convenient way of supporting multi-rate, multi-level grades of service in multimedia communications and prioritized heterogeneous networking systems. In this paper, we propose multiuser convolutional channel coding in SEMA that provides fewer cross-correlations among users and thereby reducing multiple access interference (MAI). We analyze SEMA multiuser convolutional coding in additive white Gaussian noise (AWGN) channels as well as fading channels. Our analysis includes downlink synchronous system as well as asynchronous system such as uplink mobile-to-base station communication.展开更多
To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder...To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder to improve its performance at short interleaving delay. The combination of Log MAP and SOVA avoids updating the matrices of the maximum path, and also makes a contribution to the requirement of short delay. The simulation results of several SCCCs show that the improved decoder can obtain satisfied performance with short frame interleaver and it is suitable to the high bit rate low delay communication systems.展开更多
Walsh-Hadamard transform （WriT） can solve linear error equations on Field F2, and the method can be used to recover the parameters of convolutional code. However, solving the equations with many unknowns needs enorm...Walsh-Hadamard transform （WriT） can solve linear error equations on Field F2, and the method can be used to recover the parameters of convolutional code. However, solving the equations with many unknowns needs enormous computer memory which limits the application of WriT. In order to solve this problem, a method based on segmented WriT is proposed in this paper. The coefficient vector of high dimension is reshaped and two vectors of lower dimension are obtained. Then the WriT is operated and the requirement for computer memory is much reduced. The code rate and the constraint length of convolutional code are detected from the Walsh spectrum. And the check vector is recovered from the peak position. The validity of the method is verified by the simulation result, and the performance is proved to be optimal.展开更多
In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended...In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.展开更多
In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are de...In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).展开更多
Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum err...Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.展开更多
An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matri...An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.展开更多
Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wir...Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wireless Communications. A breakthrough was definitely Turbo coding. Particularly, the concept of joining two or more convolutional encoders in parallel (PCCC) or in serial (SCCC), along with the iterative decoding technique, literally raised the expectations of the anticipated BER performance. In fact, Concatenated Convolutional Codes clearly outperform convolutional codes. Moreover, various systems, either under development or either for future use, will have high standards. The previous systems should present exceptional tolerance of noise effects and consequently a low overall number of received errors. For this purpose a new PCCC design was developed. The system’s performance analysis, using an AWGN channel, showed better results for various iterations compared to other schemes such as typical PCCC, SCCC and finally a Convolutional encoder with a Viterbi decoder.展开更多
A multiple watermarking algorithm is presented according to the multiple accessing technique of the code division multiple access （CDMA） system. Multiple watermarks are embedded into digital images in the wavelet tr...A multiple watermarking algorithm is presented according to the multiple accessing technique of the code division multiple access （CDMA） system. Multiple watermarks are embedded into digital images in the wavelet transform domain. Each of the watermarks is embedded and extracted independently without impacts to each other. Multiple watermarks are convolution encoded and block interleaved, and the orthogonal Gold sequences are used to spread spectrum of the copyright messages. CDMA encoded water-mark messages are embedded into the wavelet sub-bands excluding the wavelet HH1 sub-bands. The embedment amplitude is decided by Watson＇ s perceptual model of wavelet transform domain, and the embedmeut position in the selected wavelet sub-bands is decided randomly by a pseudo-random noise （PN） sequence. As a blind watermm＇king algorithm, watermarks are extracted without original image. The watermarking capacity of proposed algorithm is also discussed. When two watermarks are embedded in an image at the same time, the capacity is larger than the capacity when a single watermark is embedded, and is smaller than the sum of the capacity of two separately embedded watermarks. Experimental results show that the proposed algorithm improves the detection bits error rate （BER） observably, and the multiple watermarks have a preferable robustness and invisibility.展开更多
A new convolutionally coded direct sequence (DS) CDMA system is proposed. The outputs of a convolutional encoder modulate multiple band-limited DS-CDMA waveforms. The receiver detects and combines signals for the desi...A new convolutionally coded direct sequence (DS) CDMA system is proposed. The outputs of a convolutional encoder modulate multiple band-limited DS-CDMA waveforms. The receiver detects and combines signals for the desired user and feeds a soft-decision Viterbi decoder. The performance of this system is compared to that of a convolutionally coded single carrier DS CDMA system with a Rake receiver. At roughly equivalent receiver complexity, results will demonstrate superior performance of the coded multicarrier system.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
With the growth of the Internet,more and more business is being done online,for example,online offices,online education and so on.While this makes people’s lives more convenient,it also increases the risk of the netw...With the growth of the Internet,more and more business is being done online,for example,online offices,online education and so on.While this makes people’s lives more convenient,it also increases the risk of the network being attacked by malicious code.Therefore,it is important to identify malicious codes on computer systems efficiently.However,most of the existing malicious code detection methods have two problems:(1)The ability of the model to extract features is weak,resulting in poor model performance.(2)The large scale of model data leads to difficulties deploying on devices with limited resources.Therefore,this paper proposes a lightweight malicious code identification model Lightweight Malicious Code Classification Method Based on Improved SqueezeNet(LCMISNet).In this paper,the MFire lightweight feature extraction module is constructed by proposing a feature slicing module and a multi-size depthwise separable convolution module.The feature slicing module reduces the number of parameters by grouping features.The multi-size depthwise separable convolution module reduces the number of parameters and enhances the feature extraction capability by replacing the standard convolution with depthwise separable convolution with different convolution kernel sizes.In addition,this paper also proposes a feature splicing module to connect the MFire lightweight feature extraction module based on the feature reuse and constructs the lightweight model LCMISNet.The malicious code recognition accuracy of LCMISNet on the BIG 2015 dataset and the Malimg dataset reaches 98.90% and 99.58%,respectively.It proves that LCMISNet has a powerful malicious code recognition performance.In addition,compared with other network models,LCMISNet has better performance,and a lower number of parameters and computations.展开更多
The field of finance heavily relies on cybersecurity to safeguard its systems and clients from harmful software.The identification of malevolent code within financial software is vital for protecting both the financia...The field of finance heavily relies on cybersecurity to safeguard its systems and clients from harmful software.The identification of malevolent code within financial software is vital for protecting both the financial system and individual clients.Nevertheless,present detection models encounter limitations in their ability to identify malevolent code and its variations,all while encompassing a multitude of parameters.To overcome these obsta-cles,we introduce a lean model for classifying families of malevolent code,formulated on Ghost-DenseNet-SE.This model integrates the Ghost module,DenseNet,and the squeeze-and-excitation(SE)channel domain attention mechanism.It substitutes the standard convolutional layer in DenseNet with the Ghost module,thereby diminishing the model’s size and augmenting recognition speed.Additionally,the channel domain attention mechanism assigns distinctive weights to feature channels,facilitating the extraction of pivotal characteristics of malevolent code and bolstering detection precision.Experimental outcomes on the Malimg dataset indicate that the model attained an accuracy of 99.14%in discerning families of malevolent code,surpassing AlexNet(97.8%)and The visual geometry group network(VGGNet)(96.16%).The proposed model exhibits reduced parameters,leading to decreased model complexity alongside enhanced classification accuracy,rendering it a valuable asset for categorizing malevolent code.展开更多
The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function)T[x,y] of convolutional codes.Next use computer simulat...The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function)T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise(AWGN) for maximum free distance(MFD) codes of previously found and optimum distance spectrum(ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively.Finally,a method of how to search for good convolutional codes is given.展开更多
The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function) T[x,y] of convolutional codes.Next use computer simula...The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function) T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise (AWGN) for maximum free distance (MFD) codes of previously found and optimum distance spectrum (ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively. Finally,a method of how to search for good convolutional codes is given.展开更多
文摘Self-encoded spread spectrum eliminates the need for traditional pseudo noise (PN) code generators. In a self-encoded multiple access (SEMA) system, the number of users is not limited by the number of available sequences, unlike code division multiple access (CDMA) systems that employ PN codes such as m-, Gold or Kassami sequences. SEMA provides a convenient way of supporting multi-rate, multi-level grades of service in multimedia communications and prioritized heterogeneous networking systems. In this paper, we propose multiuser convolutional channel coding in SEMA that provides fewer cross-correlations among users and thereby reducing multiple access interference (MAI). We analyze SEMA multiuser convolutional coding in additive white Gaussian noise (AWGN) channels as well as fading channels. Our analysis includes downlink synchronous system as well as asynchronous system such as uplink mobile-to-base station communication.
文摘To improve the performance of the short interleaved serial concatenated convolutional code(SCCC) with low decoding iterative times, the structure of Log MAP algorithm is introduced into the conventional SOVA decoder to improve its performance at short interleaving delay. The combination of Log MAP and SOVA avoids updating the matrices of the maximum path, and also makes a contribution to the requirement of short delay. The simulation results of several SCCCs show that the improved decoder can obtain satisfied performance with short frame interleaver and it is suitable to the high bit rate low delay communication systems.
基金supported by the National Natural Science Foundation of China(1127105011371183+2 种基金61403036)the Science and Technology Development Foundation of CAEP(2013A04030202013B0403068)
基金supported by the National Natural Science Foundation of China(61072120)
文摘Walsh-Hadamard transform （WriT） can solve linear error equations on Field F2, and the method can be used to recover the parameters of convolutional code. However, solving the equations with many unknowns needs enormous computer memory which limits the application of WriT. In order to solve this problem, a method based on segmented WriT is proposed in this paper. The coefficient vector of high dimension is reshaped and two vectors of lower dimension are obtained. Then the WriT is operated and the requirement for computer memory is much reduced. The code rate and the constraint length of convolutional code are detected from the Walsh spectrum. And the check vector is recovered from the peak position. The validity of the method is verified by the simulation result, and the performance is proved to be optimal.
基金supported by the National Natural Science Foundation of China(No.61401164,No.61201145,No.61471175)the Natural Science Foundation of Guangdong Province of China(No.2014A030310308)the Supporting Plan for New Century Excellent Talents of the Ministry of Education(No.NCET-13-0805)
文摘In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.
基金the National Natural Science Foundation of China(Nos.61401164,61471131 and 61201145)the Natural Science Foundation of Guangdong Province(No.2014A030310308)
文摘In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).
基金the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Project of Shandong Province Higher Educational Science and Technology Program,China(Grant No.J18KZ012).
文摘Quantum error correction technology is an important solution to solve the noise interference generated during the operation of quantum computers.In order to find the best syndrome of the stabilizer code in quantum error correction,we need to find a fast and close to the optimal threshold decoder.In this work,we build a convolutional neural network(CNN)decoder to correct errors in the toric code based on the system research of machine learning.We analyze and optimize various conditions that affect CNN,and use the RestNet network architecture to reduce the running time.It is shortened by 30%-40%,and we finally design an optimized algorithm for CNN decoder.In this way,the threshold accuracy of the neural network decoder is made to reach 10.8%,which is closer to the optimal threshold of about 11%.The previous threshold of 8.9%-10.3%has been slightly improved,and there is no need to verify the basic noise.
基金the National Natural Science Foundation of China(No.61401164)。
文摘An algebraic construction methodology is proposed to design binary time-invariant convolutional low-density parity-check(LDPC)codes.Assisted by a proposed partial search algorithm,the polynomialform parity-check matrix of the time-invariant convolutional LDPC code is derived by combining some special codewords of an(n,2,n−1)code.The achieved convolutional LDPC codes possess the characteristics of comparatively large girth and given syndrome former memory.The objective of our design is to enable the time-invariant convolutional LDPC codes the advantages of excellent error performance and fast encoding.In particular,the error performance of the proposed convolutional LDPC code with small constraint length is superior to most existing convolutional LDPC codes.
文摘Coding techniques have always been a major area of scientific interest. Due to this interest, many coding schemes were invented. Eventually, their implementation in various systems contributed in the evolvement of Wireless Communications. A breakthrough was definitely Turbo coding. Particularly, the concept of joining two or more convolutional encoders in parallel (PCCC) or in serial (SCCC), along with the iterative decoding technique, literally raised the expectations of the anticipated BER performance. In fact, Concatenated Convolutional Codes clearly outperform convolutional codes. Moreover, various systems, either under development or either for future use, will have high standards. The previous systems should present exceptional tolerance of noise effects and consequently a low overall number of received errors. For this purpose a new PCCC design was developed. The system’s performance analysis, using an AWGN channel, showed better results for various iterations compared to other schemes such as typical PCCC, SCCC and finally a Convolutional encoder with a Viterbi decoder.
基金the National High Technology Research and Development Programme of China(No 2006AA01Z407,No.2007AA01Z478)the Postdoctoral Science Foundation of China(No.20070420707)
文摘A multiple watermarking algorithm is presented according to the multiple accessing technique of the code division multiple access （CDMA） system. Multiple watermarks are embedded into digital images in the wavelet transform domain. Each of the watermarks is embedded and extracted independently without impacts to each other. Multiple watermarks are convolution encoded and block interleaved, and the orthogonal Gold sequences are used to spread spectrum of the copyright messages. CDMA encoded water-mark messages are embedded into the wavelet sub-bands excluding the wavelet HH1 sub-bands. The embedment amplitude is decided by Watson＇ s perceptual model of wavelet transform domain, and the embedmeut position in the selected wavelet sub-bands is decided randomly by a pseudo-random noise （PN） sequence. As a blind watermm＇king algorithm, watermarks are extracted without original image. The watermarking capacity of proposed algorithm is also discussed. When two watermarks are embedded in an image at the same time, the capacity is larger than the capacity when a single watermark is embedded, and is smaller than the sum of the capacity of two separately embedded watermarks. Experimental results show that the proposed algorithm improves the detection bits error rate （BER） observably, and the multiple watermarks have a preferable robustness and invisibility.
文摘A new convolutionally coded direct sequence (DS) CDMA system is proposed. The outputs of a convolutional encoder modulate multiple band-limited DS-CDMA waveforms. The receiver detects and combines signals for the desired user and feeds a soft-decision Viterbi decoder. The performance of this system is compared to that of a convolutionally coded single carrier DS CDMA system with a Rake receiver. At roughly equivalent receiver complexity, results will demonstrate superior performance of the coded multicarrier system.
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With the growth of the Internet,more and more business is being done online,for example,online offices,online education and so on.While this makes people’s lives more convenient,it also increases the risk of the network being attacked by malicious code.Therefore,it is important to identify malicious codes on computer systems efficiently.However,most of the existing malicious code detection methods have two problems:(1)The ability of the model to extract features is weak,resulting in poor model performance.(2)The large scale of model data leads to difficulties deploying on devices with limited resources.Therefore,this paper proposes a lightweight malicious code identification model Lightweight Malicious Code Classification Method Based on Improved SqueezeNet(LCMISNet).In this paper,the MFire lightweight feature extraction module is constructed by proposing a feature slicing module and a multi-size depthwise separable convolution module.The feature slicing module reduces the number of parameters by grouping features.The multi-size depthwise separable convolution module reduces the number of parameters and enhances the feature extraction capability by replacing the standard convolution with depthwise separable convolution with different convolution kernel sizes.In addition,this paper also proposes a feature splicing module to connect the MFire lightweight feature extraction module based on the feature reuse and constructs the lightweight model LCMISNet.The malicious code recognition accuracy of LCMISNet on the BIG 2015 dataset and the Malimg dataset reaches 98.90% and 99.58%,respectively.It proves that LCMISNet has a powerful malicious code recognition performance.In addition,compared with other network models,LCMISNet has better performance,and a lower number of parameters and computations.
基金funded by National Natural Science Foundation of China(under Grant No.61905201)。
文摘The field of finance heavily relies on cybersecurity to safeguard its systems and clients from harmful software.The identification of malevolent code within financial software is vital for protecting both the financial system and individual clients.Nevertheless,present detection models encounter limitations in their ability to identify malevolent code and its variations,all while encompassing a multitude of parameters.To overcome these obsta-cles,we introduce a lean model for classifying families of malevolent code,formulated on Ghost-DenseNet-SE.This model integrates the Ghost module,DenseNet,and the squeeze-and-excitation(SE)channel domain attention mechanism.It substitutes the standard convolutional layer in DenseNet with the Ghost module,thereby diminishing the model’s size and augmenting recognition speed.Additionally,the channel domain attention mechanism assigns distinctive weights to feature channels,facilitating the extraction of pivotal characteristics of malevolent code and bolstering detection precision.Experimental outcomes on the Malimg dataset indicate that the model attained an accuracy of 99.14%in discerning families of malevolent code,surpassing AlexNet(97.8%)and The visual geometry group network(VGGNet)(96.16%).The proposed model exhibits reduced parameters,leading to decreased model complexity alongside enhanced classification accuracy,rendering it a valuable asset for categorizing malevolent code.
文摘The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function)T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise(AWGN) for maximum free distance(MFD) codes of previously found and optimum distance spectrum(ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively.Finally,a method of how to search for good convolutional codes is given.
文摘The paper introduces the state reduction algorithm and accelerated state reduction algorithm are used to compute the distance weight enumerator(transfer function) T[x,y] of convolutional codes.Next use computer simulation to compare upper bound on the bit error probability on an additive white Gaussian noise (AWGN) for maximum free distance (MFD) codes of previously found and optimum distance spectrum (ODS) codes with rate 1/4,overall constraint length are 5 and 7,respectively. Finally,a method of how to search for good convolutional codes is given.
