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
This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shif...This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.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 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
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
Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key ...Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key techniques: a low-complexity cyclic redundancy check(CRC) aided list successive cancellation(CALSC) decoder and a soft information calculation method. At the relay node, a low-complexity CALSC decoder is designed to reduce the computational complexity by adjusting the list size according to the reliabilities of decoded bits. Based on the path probability metric of the CALSC decoder, we propose a method to compute the soft information of the decoded bits in CALSC. Simulation results show that our proposed scheme outperforms the soft DF based on low-density parity-check codes and the soft DF with belief propagation or soft cancellation decoder, especially in the case when the source-relay channel is at the high signal-to-ratio region.展开更多
This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on hal...This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on half-duplex mode. Then, we give out receiving diversity relay scheme and coding diversity relay scheme, and present their jointly decoding methods. Furthermore, we discuss the performance of the two schemes with different power allocation coefficients. Simulations show that our relay schemes can achieve different gain with the help of relay node. And, we should allocate power to source node to just guarantee relay node can decode successfully, and allocate remain power to relay node as far as possible. In this way, this DF relay system not only achieves diversity gain, but also achieves higher and smooth spectrum efficiency.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
In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is a...In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is applied, two time slots are sufficient for one round information exchange. In this paper, we present a decode-and-forward(DF) scheme based on joint LDPC decoding for three-way relay channels, where relay decoder partially decodes the network code rather than fully decodes all the user messages. Simulation results show that the new DF scheme considerably outperforms other common schemes in three-way relay fading channels.展开更多
Network Coding (NC) is a recent technique which is used to improve the transmission data rate and the power efficiency. These goals are obtained by combining data together before transmitting them, resulting to less t...Network Coding (NC) is a recent technique which is used to improve the transmission data rate and the power efficiency. These goals are obtained by combining data together before transmitting them, resulting to less transmitted data that carry the same amount of information. NC research work over the physical layer and the upper layers are popular and needed to be more investigated. In this paper, we propose a practical system of large-number of connected multi-source network coding (LMSNC), at the physical layer that exploits the broadcast nature of the wireless channel, using the practical and bandwidth-efficient schemes decode-and-forward (DF) and then compare it with Amplify and Forward (AF). The theoretical analysis and the simulation results show the effect of the noise when it cumulates in AF system and how DF is solving this severe default. Moreover, we consider the MSNC for Small-number of connected sources (SMSNC) and the two-way communication setup where two users exchange their information over an intermediate network node (ideally called Base Station), as two reference cases to compare with. With SMSNC, the number of necessary downlink transmissions from the intermediate node to the users is reduced, and thus the throughput is increased. Simulation results obtained using high-performance non-binary turbo codes, based on Partial Unit Memory (PUM) codes (4, 2, 1, 4) and (8, 4, 3, 8);confirm that combining PUM Turbo Code (PUMTC) and NC in the proposed MSNC setup gives almost the same BER performance as that for SMSNC at the small number of processing steps mainly when PUMTC (8, 4, 3, 8) is performed, which is required to retrieve the received coded messages. In the scenario of AF, combining packets results to cumulate the noise, which justifies the reason we decided to increase the number of transmitted coded messages in the network, i.e., the BER performance improves when sending extra coded messages. Finally, the possibility for a trade-off among BER, data rate and the number of transmitted coded messages is shown for LMSNC through graphics and simulation results.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 Base Station (BS) or access point is the building block of wireless networks, so, we propose exploiting it together with the Network Coding (NC) principle. NC suffers from the complexity of the decoding processes,...The Base Station (BS) or access point is the building block of wireless networks, so, we propose exploiting it together with the Network Coding (NC) principle. NC suffers from the complexity of the decoding processes, i.e., complicated Jordan Gaussian Elimination (JGE) processes. So, this paper proposes a deterministic NC algorithm to reduce the number of sequential network decoding steps, and hence minimizing the complexity of JGE process resulting to better time delay and processing time. We propose an algorithm that combines higher number of the transmitted packets resulting to better data-rate but worse Bet Error Rate (BER). However, using such strong Forward error correction channel code, which is Partial Unit Memory Turbo Code (PUMTC) results to minimize the losses in the BER to a very acceptable lever, in fact, in Decode-and-Forward (DF) BS, the BER can be regarded as minimum. Simulation results, for both Amplify-and-Forward (AF) and DF BS schemes using PUMTC based on (8, 4, 3, 8) component codes, confirm that using PUMTC mitigates the problem of noise aggregation resulting from applying NC in the proposed schemes.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
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This work investigates the performance of various forward error correction codes, by which the MIMO-OFDM system is deployed. To ensure fair investigation, the performance of four modulations, namely, binary phase shift keying(BPSK), quadrature phase shift keying(QPSK), quadrature amplitude modulation(QAM)-16 and QAM-64 with four error correction codes(convolutional code(CC), Reed-Solomon code(RSC)+CC, low density parity check(LDPC)+CC, Turbo+CC) is studied under three channel models(additive white Guassian noise(AWGN), Rayleigh, Rician) and three different antenna configurations(2×2, 2×4, 4×4). The bit error rate(BER) and the peak signal to noise ratio(PSNR) are taken as the measures of performance. The binary data and the color image data are transmitted and the graphs are plotted for various modulations with different channels and error correction codes. Analysis on the performance measures confirm that the Turbo + CC code in 4×4 configurations exhibits better performance.
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 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.
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.61171099,No.61671080),Nokia Beijing Bell lab
文摘Soft decode-and-forward(DF) can combine the advantages of both amplify-and-forward and hard DF in relay channels. In this paper, we propose a low-complexity soft DF scheme based on polar codes, which features two key techniques: a low-complexity cyclic redundancy check(CRC) aided list successive cancellation(CALSC) decoder and a soft information calculation method. At the relay node, a low-complexity CALSC decoder is designed to reduce the computational complexity by adjusting the list size according to the reliabilities of decoded bits. Based on the path probability metric of the CALSC decoder, we propose a method to compute the soft information of the decoded bits in CALSC. Simulation results show that our proposed scheme outperforms the soft DF based on low-density parity-check codes and the soft DF with belief propagation or soft cancellation decoder, especially in the case when the source-relay channel is at the high signal-to-ratio region.
文摘This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on half-duplex mode. Then, we give out receiving diversity relay scheme and coding diversity relay scheme, and present their jointly decoding methods. Furthermore, we discuss the performance of the two schemes with different power allocation coefficients. Simulations show that our relay schemes can achieve different gain with the help of relay node. And, we should allocate power to source node to just guarantee relay node can decode successfully, and allocate remain power to relay node as far as possible. In this way, this DF relay system not only achieves diversity gain, but also achieves higher and smooth spectrum efficiency.
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supported in part by the National Natural Science Foundation of China under Grant 61201187by the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions under Grant YETP0110+2 种基金by the Tsinghua University Initiative Scientific Research Program under Grant 20121088074by the Foundation of Zhejiang Educational Committee under Grant Y201121579by the Visiting Scholar Professional Development Project of Zhejiang Educational Committee under Grant FX2014052
文摘In this paper a low-density pairwise check(LDPC) coded three-way relay system is considered, where three user nodes desire to exchange messages with the help of one relay node. Since physical-layer network coding is applied, two time slots are sufficient for one round information exchange. In this paper, we present a decode-and-forward(DF) scheme based on joint LDPC decoding for three-way relay channels, where relay decoder partially decodes the network code rather than fully decodes all the user messages. Simulation results show that the new DF scheme considerably outperforms other common schemes in three-way relay fading channels.
文摘Network Coding (NC) is a recent technique which is used to improve the transmission data rate and the power efficiency. These goals are obtained by combining data together before transmitting them, resulting to less transmitted data that carry the same amount of information. NC research work over the physical layer and the upper layers are popular and needed to be more investigated. In this paper, we propose a practical system of large-number of connected multi-source network coding (LMSNC), at the physical layer that exploits the broadcast nature of the wireless channel, using the practical and bandwidth-efficient schemes decode-and-forward (DF) and then compare it with Amplify and Forward (AF). The theoretical analysis and the simulation results show the effect of the noise when it cumulates in AF system and how DF is solving this severe default. Moreover, we consider the MSNC for Small-number of connected sources (SMSNC) and the two-way communication setup where two users exchange their information over an intermediate network node (ideally called Base Station), as two reference cases to compare with. With SMSNC, the number of necessary downlink transmissions from the intermediate node to the users is reduced, and thus the throughput is increased. Simulation results obtained using high-performance non-binary turbo codes, based on Partial Unit Memory (PUM) codes (4, 2, 1, 4) and (8, 4, 3, 8);confirm that combining PUM Turbo Code (PUMTC) and NC in the proposed MSNC setup gives almost the same BER performance as that for SMSNC at the small number of processing steps mainly when PUMTC (8, 4, 3, 8) is performed, which is required to retrieve the received coded messages. In the scenario of AF, combining packets results to cumulate the noise, which justifies the reason we decided to increase the number of transmitted coded messages in the network, i.e., the BER performance improves when sending extra coded messages. Finally, the possibility for a trade-off among BER, data rate and the number of transmitted coded messages is shown for LMSNC through graphics and simulation results.
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.
文摘The Base Station (BS) or access point is the building block of wireless networks, so, we propose exploiting it together with the Network Coding (NC) principle. NC suffers from the complexity of the decoding processes, i.e., complicated Jordan Gaussian Elimination (JGE) processes. So, this paper proposes a deterministic NC algorithm to reduce the number of sequential network decoding steps, and hence minimizing the complexity of JGE process resulting to better time delay and processing time. We propose an algorithm that combines higher number of the transmitted packets resulting to better data-rate but worse Bet Error Rate (BER). However, using such strong Forward error correction channel code, which is Partial Unit Memory Turbo Code (PUMTC) results to minimize the losses in the BER to a very acceptable lever, in fact, in Decode-and-Forward (DF) BS, the BER can be regarded as minimum. Simulation results, for both Amplify-and-Forward (AF) and DF BS schemes using PUMTC based on (8, 4, 3, 8) component codes, confirm that using PUMTC mitigates the problem of noise aggregation resulting from applying NC in the proposed schemes.
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.
