Binary code signals have been widely used in various radars due to their simpleimplementation,but the selection of the binary codes with high comporession ratio and lowsidelobes is not solved well,because of the diffi...Binary code signals have been widely used in various radars due to their simpleimplementation,but the selection of the binary codes with high comporession ratio and lowsidelobes is not solved well,because of the difficult processing in mathmatics and expensivecalculation cost.In this paper,neural computing is introduced into the field of the selection ofbinary codes and a new method based’on simulated annealing(SA)is proposed.The experimentsshow that the proposed method is able to select the optimal binary codes with much less timecost than the known methods,furhtermore the optimization selection of the binary codes versusthe calculation cost tradeoff is easier.展开更多
Although the distance between binary codes can be computed fast in Hamming space, linear search is not practical for large scale datasets. Therefore attention has been paid to the efficiency of performing approximate ...Although the distance between binary codes can be computed fast in Hamming space, linear search is not practical for large scale datasets. Therefore attention has been paid to the efficiency of performing approximate nearest neighbor search, in which hierarchical clustering trees （HCT） are widely used. However, HCT select cluster centers randomly and build indexes with the entire binary code, this degrades search performance. In this paper, we first propose a new clustering algorithm, which chooses cluster centers on the basis of relative distances and uses a more homogeneous partition of the dataset than HCT has to build the hierarchical clustering trees. Then, we present an algorithm to compress binary codes by extracting distinctive bits according to the standard deviation of each bit. Consequently, a new index is proposed using compressed binary codes based on hierarchical decomposition of binary spaces. Experiments conducted on reference datasets and a dataset of one billion binary codes demonstrate the effectiveness and efficiency of our method.展开更多
In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of inform...In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of information technology.A matrix decoding method is proposed in this paper.The method is a universal data reconstruction scheme for erasure codes over binary fields.Besides a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors.Data reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer codes.And more,it can be applied to other non-binary fields easily,so it is expected that the method has an extensive application in the future.展开更多
This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary qua...This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.展开更多
A binary tree can be represented by a code reflecting the traversal of the corresponding regular binary tree in given monotonic order. A different coding scheme based on the branches of a regular binary tree with n-no...A binary tree can be represented by a code reflecting the traversal of the corresponding regular binary tree in given monotonic order. A different coding scheme based on the branches of a regular binary tree with n-nodes is proposed. It differs from the coding scheme generally used and makes no distinction between internal nodes and terminal nodes. A code of a regular binary tree with nnodes is formed by labeling the left branches by O’s and the right branches by l’s and then traversing these branches in pre-order. Root is always assumed to be on a left branch.展开更多
Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal...Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.展开更多
A new non-binary decoding method, which is called Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the ...A new non-binary decoding method, which is called Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the convolutional encoder. Yaletharatalhussein decoding algorithm outperforms the Viterbi algorithm and other algorithms in its simplicity, very small computational complexity, decoding reliability for high states TCM codes that suitable for Fourth-Generation (4G), decreasing errors with increasing word length, and easy to implement with real-time applications. The proposed Yaletharatalhussein decoding algorithm deals with non-binary error control coding of the convolutional and TCM codes. Convolutional codes differ from block codes in that a block code takes a fixed message length and encodes it, whereas a convolutional code can encode a continuous stream of data, and a hard-decision decoding can easily be realized using the Yaletharatalhussein algorithm. The idea of non-binary codes has been extended for symbols defined over rings of integers, which outperform binary codes with only a small increase in decoding complexity. The simulation results show that the performance of the nonbinary TCM-based Yaletharatalhussein algorithm outperforms the binary and non-binary decoding methods.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
The self-orthogonal condition is analyzed with respect to symplectic inner product for the binary code that generated by [B1 I B2 B3],where Bi are the binary n ×n matrices,I is an identity matrix.By the use of th...The self-orthogonal condition is analyzed with respect to symplectic inner product for the binary code that generated by [B1 I B2 B3],where Bi are the binary n ×n matrices,I is an identity matrix.By the use of the binary codes that generated by [B1 I B2 B2B1^T],asymptotic good[[2n ,n ]]additive quantum codes are obtained.展开更多
A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several conseq...A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.展开更多
In the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting err...In the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting errors of the channel A is presented.展开更多
文摘Binary code signals have been widely used in various radars due to their simpleimplementation,but the selection of the binary codes with high comporession ratio and lowsidelobes is not solved well,because of the difficult processing in mathmatics and expensivecalculation cost.In this paper,neural computing is introduced into the field of the selection ofbinary codes and a new method based’on simulated annealing(SA)is proposed.The experimentsshow that the proposed method is able to select the optimal binary codes with much less timecost than the known methods,furhtermore the optimization selection of the binary codes versusthe calculation cost tradeoff is easier.
文摘Although the distance between binary codes can be computed fast in Hamming space, linear search is not practical for large scale datasets. Therefore attention has been paid to the efficiency of performing approximate nearest neighbor search, in which hierarchical clustering trees （HCT） are widely used. However, HCT select cluster centers randomly and build indexes with the entire binary code, this degrades search performance. In this paper, we first propose a new clustering algorithm, which chooses cluster centers on the basis of relative distances and uses a more homogeneous partition of the dataset than HCT has to build the hierarchical clustering trees. Then, we present an algorithm to compress binary codes by extracting distinctive bits according to the standard deviation of each bit. Consequently, a new index is proposed using compressed binary codes based on hierarchical decomposition of binary spaces. Experiments conducted on reference datasets and a dataset of one billion binary codes demonstrate the effectiveness and efficiency of our method.
基金supported by the National Natural Science Foundation of China under Grant No.61501064Sichuan Provincial Science and Technology Project under Grant No.2016GZ0122
文摘In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of information technology.A matrix decoding method is proposed in this paper.The method is a universal data reconstruction scheme for erasure codes over binary fields.Besides a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors.Data reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer codes.And more,it can be applied to other non-binary fields easily,so it is expected that the method has an extensive application in the future.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 11071255） and Science Foundation for young teachers in Science College, Air Force Engineering University. The authors are very grateful to the anonymous referees and the editors for their valuable comments and suggestions, which help to improve the manuscript significantly.
文摘This paper discusses optimal binary codes and pure binary quantum codes created using Steane construction. First, a local search algorithm for a special subclass of quasi-cyclic codes is proposed, then five binary quasi-cyclic codes are built. Second, three classical construction methods are generalized for new codes from old such that they are suitable for constructing binary self-orthogonal codes, and 62 binary codes and six subcode chains of obtained self-orthogonal codes are designed. Third, six pure binary quantum codes are constructed from the code pairs obtained through Steane construction. There are 66 good binary codes that include 12 optimal linear codes, 45 known optimal linear codes, and nine known optimal self-orthogonal codes. The six pure binary quantum codes all achieve the performance of their additive counterparts constructed by quaternary construction and thus are known optimal codes.
文摘A binary tree can be represented by a code reflecting the traversal of the corresponding regular binary tree in given monotonic order. A different coding scheme based on the branches of a regular binary tree with n-nodes is proposed. It differs from the coding scheme generally used and makes no distinction between internal nodes and terminal nodes. A code of a regular binary tree with nnodes is formed by labeling the left branches by O’s and the right branches by l’s and then traversing these branches in pre-order. Root is always assumed to be on a left branch.
文摘Cyclic codes form an important class of codes. They have very interesting algebraic structure. Furthermore, they are equivalent to many important codes, such as binary Hamming codes, Golay codes and BCH codes. Minimal codewords in linear codes are widely used in constructing decoding algorithms and studying linear secret sharing scheme. In this paper, we show that in the binary cyclic code all of the codewords are minimal, except 0 and 1. Then, we obtain a result about the number of minimal codewords in the binary cyclic codes.
文摘A new non-binary decoding method, which is called Yaletharatalhussein decoding algorithm, is designed and implemented for decoding non-binary convolutional codes which is based on the trellis diagram representing the convolutional encoder. Yaletharatalhussein decoding algorithm outperforms the Viterbi algorithm and other algorithms in its simplicity, very small computational complexity, decoding reliability for high states TCM codes that suitable for Fourth-Generation (4G), decreasing errors with increasing word length, and easy to implement with real-time applications. The proposed Yaletharatalhussein decoding algorithm deals with non-binary error control coding of the convolutional and TCM codes. Convolutional codes differ from block codes in that a block code takes a fixed message length and encodes it, whereas a convolutional code can encode a continuous stream of data, and a hard-decision decoding can easily be realized using the Yaletharatalhussein algorithm. The idea of non-binary codes has been extended for symbols defined over rings of integers, which outperform binary codes with only a small increase in decoding complexity. The simulation results show that the performance of the nonbinary TCM-based Yaletharatalhussein algorithm outperforms the binary and non-binary decoding methods.
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）.
文摘The self-orthogonal condition is analyzed with respect to symplectic inner product for the binary code that generated by [B1 I B2 B3],where Bi are the binary n ×n matrices,I is an identity matrix.By the use of the binary codes that generated by [B1 I B2 B2B1^T],asymptotic good[[2n ,n ]]additive quantum codes are obtained.
基金The work was supported in part by Harbin Normal University's Natural Scientific fund items (KM2006-20 and KM2005-14)Educational department scientific Technology item (1151112)Postdoctorate's fund item (LRB-KY01043)Scientific Technology Brainstorm item in Hei Longjiang province
文摘A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n, k, d]] is given by using classical binary codes with specific properties in F2^3n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.
文摘In the present work, a construction making possible creation of an additive channel of cardinality s and rank r for arbitrary integers s, r, n (r≤min (n,s-1)), as well as creation of a code correcting errors of the channel A is presented.
