Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to im...Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.展开更多
A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbo...A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern＇s order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.展开更多
In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all ...In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.展开更多
In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDP...In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.展开更多
Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from...Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks.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
This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theor...This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.展开更多
A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorit...A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.展开更多
In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differen...In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.展开更多
It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its des...It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.展开更多
A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L ...A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.展开更多
We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum error...We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.展开更多
In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit c...In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits （Shor code, Steane code and five stable subcode）, it shows obvious superiority in the quantum coding efficiency and transmission efficiency.展开更多
When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum sig...When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.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
Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I 1∩I 2∩.....Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I 1∩I 2∩...∩I n for the information bit, embed R/J i into R/I 1∩I 2∩...∩I n, and asssign the cosets of R/J i as the subring of R/I 1∩I 2∩...∩I n and the cosets of R/J i in R/I 1∩I 2∩...∩I n as check lines. There exist many code classes in Chinese Remainder Codes, which have high code rates. Chinese Remainder Codes are the essential generalization of Sun Zi Codes.展开更多
This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the propertie...This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.展开更多
Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to ...Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.展开更多
In 1993, Alabhadi and Wicker gave a modification to Xinmei Digital Signature Scheme based on error-correcting codes, which is usually denoted by AW Scheme. In this paper we show that the AW Scheme is actually not secu...In 1993, Alabhadi and Wicker gave a modification to Xinmei Digital Signature Scheme based on error-correcting codes, which is usually denoted by AW Scheme. In this paper we show that the AW Scheme is actually not secure: anyone holding public keys of the signatory can obtain the equivalent private keys, and then forge digital signatures for arbitrary messages successfully. We also point out that one can hardly construct a digital signature scheme with high-level security due to the difficulty of decomposing large matrixes.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072071)
文摘Quantum secret sharing（QSS） is a procedure of sharing classical information or quantum information by using quantum states. This paper presents how to use a [2k- 1, 1, k] quantum error-correcting code （QECC） to implement a quantum （k, 2k-1） threshold scheme. It also takes advantage of classical enhancement of the [2k-1, 1, k] QECC to establish a QSS scheme which can share classical information and quantum information simultaneously. Because information is encoded into QECC, these schemes can prevent intercept-resend attacks and be implemented on some noisy channels.
文摘A novel low-complexity weighted symbol-flipping algorithm with flipping patterns to decode nonbinary low-density parity-check codes is proposed. The proposed decoding procedure updates the hard-decision received symbol vector iteratively in search of a valid codeword in the symbol vector space. Only one symbol is flipped in each iteration, and symbol flipping function, which is employed as the symbol flipping metric, combines the number of failed checks and the reliabilities of the received bits and calculated symbols. A scheme to avoid infinite loops and select one symbol to flip in high order Galois field search is also proposed. The design of flipping pattern＇s order and depth, which is dependent of the computational requirement and error performance, is also proposed and exemplified. Simulation results show that the algorithm achieves an appealing tradeoff between performance and computational requirement over relatively low Galois field for short to medium code length.
基金supported in part by National Basic Research Program of China under Grant No.2012CB316100National Natural Science Foundation of China under Grants 61372074 and 91438101+1 种基金Joint Funds of the National Natural Science Foundation of China under Grant No.U1504601Science and Technology on Communication Networks Laboratory under Grant KX132600032
文摘In this paper, we study the rank of matrices over GF(2~p),and propose two construction methods for algebraic-based nonbinary LDPC codes from an existing LDPC code, referred to as the original code. By multiplying all elements of each column of the binary parity-check matrix H corresponding to the original code with the same nonzero element of any field, the first class of nonbinary LDPC codes with flexible field order is proposed. The second method is to replace the nonzero elements of some columns in H with different nonzero field elements in a given field, and then another class of nonbinary LDPC codes with various rates is obtained. Simulation results show that the proposed nonbinary LDPC codes perform well over the AWGN channel with the iterative decoding algorithms.
基金supported in part by National Natural Science Foundation of China under Grants 61372074,91438101,61103143,U1504601,and U1404622Key Scientific and Technological Project of Henan under Grants 162102310589 and 172102310124
文摘In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.
基金This work was supported in part by the National Science Foundation of China(No.61772539,6187212,61972405),STITSX(No.201705D131025),1331KITSX,and CiCi3D.
文摘Stereolithographic(STL)files have been extensively used in rapid prototyping industries as well as many other fields as watermarking algorithms to secure intellectual property and protect three-dimensional models from theft.However,to the best of our knowledge,few studies have looked at how watermarking can resist attacks that involve vertex-reordering.Here,we present a lossless and robust watermarking scheme for STL files to protect against vertexreordering attacks.Specifically,we designed a novel error-correcting code(ECC)that can correct the error of any one-bit in a bitstream by inserting several check digits.In addition,ECC is designed to make use of redundant information according to the characteristics of STL files,which introduces further robustness for defense against attacks.No modifications are made to the geometric information of the three-dimensional model,which respects the requirements of a highprecision model.The experimental results show that the proposed watermarking scheme can survive numerous kinds of attack,including rotation,scaling and translation(RST),facet reordering,and vertex-reordering attacks.
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.
基金Supported by Trans-century Training Program Foundation for the Talents by the State Education Commission
文摘This paper proved the statement that a good linear block encoder is in fact a good local-random sequence generator. Furthermore, this statement discovers the deep relationship between the error-correcting coding theory and the modern cryptography.
基金Supported by the National High Technology Research and Development Programme of China(No.2009AAJ128,2009AAJ208,2010AA7010422)
文摘A hybrid decoding algorithm is proposed for nonbinary low-density parity-check （LDPC） codes, which combines the weighted symbol-flipping （WSF） algorithm with the fast Fourier trans- form q-ary sum-product algorithm （FFT-QSPA）. The flipped position and value are determined by the symbol flipping metric and the received bit values in the first stage WSF algorithm. If the low- eomplexity WSF algorithm is failed, the second stage FFT-QSPA is activated as a switching strategy. Simulation results show that the proposed hybrid algorithm greatly reduces the computational complexity with the performance close to that of FFT-QSPA.
文摘In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.
基金Supported by the National Natural Science Foundation of China (No.60403004)the Outstanding Youth Foundation of China (No.0612000500)
文摘It is a regular way of constructing quantum error-correcting codes via codes with self-orthogonal property, and whether a classical Bose-Chaudhuri-Hocquenghem (BCH) code is self-orthogonal can be determined by its designed distance. In this paper, we give the sufficient and necessary condition for arbitrary classical BCH codes with self-orthogonal property through algorithms. We also give a better upper bound of the designed distance of a classical narrow-sense BCH code which contains its Euclidean dual. Besides these, we also give one algorithm to compute the dimension of these codes. The complexity of all algorithms is analyzed. Then the results can be applied to construct a series of quantum BCH codes via the famous CSS constructions.
基金The National Natural Science Foundation of China (No60472018)
文摘A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.
基金Supported by the National Natural Science Foundation of China under Grant No.61170321the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20110092110024the Scientific Research Innovation Plan for College Graduates of Jiangsu Province under Grant No.CXZZ13 0105
文摘We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.
基金Supported by the National Natural Science Foundation of China (61271122)the Natural Science Foundation of Anhui Province(1208085MF102)
文摘In this paper, the cyclic code of the classic circuit is transformed and transplanted; then, the quantum encoding scheme based on cyclic code and quantum error-correction circuit is constructed. The proposed circuit can correct one-bit error, and the use of redundant bits to encode more than one-bit quantum information breaks the previous limitations of many bits encoding a quantum bit. Compared with the existing coding circuits （Shor code, Steane code and five stable subcode）, it shows obvious superiority in the quantum coding efficiency and transmission efficiency.
基金The project supported by National Natural Science Foundation of China under Grant No. 60472018, and the Foundation of National Laboratory for Modern Communications
文摘When the time variable in quantum signal processing is discrete, the Fourier transform exists on the vector space of n-tuples over the Galois field F2, which plays an important role in the investigation of quantum signals. By using Fourier transforms, the idea of quantum coding theory can be described in a setting that is much different from that seen that far. Quantum BCH codes can be defined as codes whose quantum states have certain specified consecutive spectral components equal to zero and the error-correcting ability is also described by the number of the consecutive zeros. Moreover, the decoding of quantum codes can be described spectrally with more efficiency.
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.
文摘Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I 1∩I 2∩...∩I n for the information bit, embed R/J i into R/I 1∩I 2∩...∩I n, and asssign the cosets of R/J i as the subring of R/I 1∩I 2∩...∩I n and the cosets of R/J i in R/I 1∩I 2∩...∩I n as check lines. There exist many code classes in Chinese Remainder Codes, which have high code rates. Chinese Remainder Codes are the essential generalization of Sun Zi Codes.
文摘This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.
基金The project supported by National Natural Science Foundation of China under Grant Nos.60472018 and 60573127partly supported by the Postdoctoral Science Foundation of Central South University
文摘Exploiting the encoding process of the stabilizer quantum code [[n, k, d]], a deterministic quantum communication scheme, in which n - 1 photons are distributed forward and backward in two-way channel, is proposed to transmit the secret messages with unconditional security. The present scheme can be implemented to distribute the secret quantum （or classical） messages with great capacity in imperfect quantum channel since the utilized code encodes k-qubit messages for each scheme run.
基金This work was supported by the National Key Foundation Research "973" Project (Grant No.G1999035802) and National Science Fund for Distinguished Young Scholars (Grant No. 60025205).
文摘In 1993, Alabhadi and Wicker gave a modification to Xinmei Digital Signature Scheme based on error-correcting codes, which is usually denoted by AW Scheme. In this paper we show that the AW Scheme is actually not secure: anyone holding public keys of the signatory can obtain the equivalent private keys, and then forge digital signatures for arbitrary messages successfully. We also point out that one can hardly construct a digital signature scheme with high-level security due to the difficulty of decomposing large matrixes.
