For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. ...For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.展开更多
A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the we...A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.展开更多
Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Seri...Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, which proves its efficiency.展开更多
Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results s...Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results show that the ECC did improve the performance dramatically,with the SEU cross sections of SRAMs with ECC being at the order of 10^(-11) cm^2/bit,two orders of magnitude higher than that without ECC(at the order of 10^(-9) cm^2/bit).Also,ineffectiveness of ECC module,including 1-,2- and 3-bits errors in single word(not Multiple Bit Upsets),was detected.The ECC modules in SRAMs utilizing(12,8) Hamming code would lose work when 2-bits upset accumulates in one codeword.Finally,the probabilities of failure modes involving 1-,2- and 3-bits errors,were calcaulated at 39.39%,37.88%and 22.73%,respectively,which agree well with the experimental results.展开更多
In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary ...In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.展开更多
纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Cor...纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Correction Code,ECC)改造基本HFE(Hidden Field Equations)密码算法,所得的新密码算法具有纠错和加密功能,而且因其具有概率密码特性以及建立在MQ困难问题之上,具有很高的安全强度。展开更多
In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the genera...In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.展开更多
In deep sub-micron ICs, growing amounts of on-die memory and scaling effects make embedded memories more vulnerable to reliability problems, such as soft errors induced by radiation. Error Correction Code(ECC) along w...In deep sub-micron ICs, growing amounts of on-die memory and scaling effects make embedded memories more vulnerable to reliability problems, such as soft errors induced by radiation. Error Correction Code(ECC) along with scrubbing is an efficient method for protecting memories against these errors. However, the latency of coding circuits brings speed penalties in high performance applications. This paper proposed a "bit bypassing" ECC protected memory by buffering the encoded data and adding an identifying address for the input data. The proposed memory design has been fabricated on a 130 nm CMOS process. According to the measurement, the proposed scheme only gives the minimum delay overhead of 22.6%, compared with other corresponding memories. Furthermore, heavy ion testing demonstrated the single event effects performance of the proposed memory achieves error rate reductions by 42.9 to 63.3 times.展开更多
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved i...The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.展开更多
In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received w...In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.60972046)Grant from the National Defense Pre-Research Foundation of China
文摘For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.
基金Sponsored by the Ministerial Level Advanced Research Foundation (20304)
文摘A new Chien search method for shortened Reed-Solomon （RS） code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array （FPGA） xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s.
文摘Genetic algorithms are successfully used for decoding some classes of error correcting codes, and offer very good performances for solving large optimization problems. This article proposes a new decoder based on Serial Genetic Algorithm Decoder (SGAD) for decoding Low Density Parity Check (LDPC) codes. The results show that the proposed algorithm gives large gains over sum-product decoder, which proves its efficiency.
基金Supported by the National Natural Science Foundation of China(Nos.11079045 and 11179003)the Important Direction Project of the CAS Knowledge Innovation Program(No.KJCX2-YW-N27)
文摘Single event upsets(SEUs) induced by heavy ions were observed in 65 nm SRAMs to quantitatively evaluate the applicability and effectiveness of single-bit error correcting code(ECC) utilizing Hamming Code.The results show that the ECC did improve the performance dramatically,with the SEU cross sections of SRAMs with ECC being at the order of 10^(-11) cm^2/bit,two orders of magnitude higher than that without ECC(at the order of 10^(-9) cm^2/bit).Also,ineffectiveness of ECC module,including 1-,2- and 3-bits errors in single word(not Multiple Bit Upsets),was detected.The ECC modules in SRAMs utilizing(12,8) Hamming code would lose work when 2-bits upset accumulates in one codeword.Finally,the probabilities of failure modes involving 1-,2- and 3-bits errors,were calcaulated at 39.39%,37.88%and 22.73%,respectively,which agree well with the experimental results.
文摘In this paper, we present a novel technique based on a mixed Error Correcting Code(ECC)-the convolutional code and the repetition code to enhance the robustness of the embedded watermark. Before embedding, the binary watermark is scanned to one-dimension sequence and later inputted into the (3, 1, 2) convolutional encoder and (3, 1) repetition encoder frame by frame, which will improve the error correcting capability of decoder. The output code sequence is scanned to some matrixes as the new watermark messages. The watermarking is selected in low frequency band of the Discrete Wavelet Transform (DWT) and therefore it can resist the destruction of image processing. Experimental results are presented to demonstrate that the robustness of a watermark with mixed ECC is much higher than the traditional one just with repetition coding while suffering JPEG lossy compression, salt and pepper noise and center cutting processing.
文摘纠错密码是一种利用纠错码体制来实现纠错和加密双重功能的一种密码体制。大部分已知的纠错密码从变换的角度看是一种对明文的线性变换。从密码分析的角度看,由于不具有非线性变换,密码的混淆能力不强,容易被攻击。利用纠错码(Error-Correction Code,ECC)改造基本HFE(Hidden Field Equations)密码算法,所得的新密码算法具有纠错和加密功能,而且因其具有概率密码特性以及建立在MQ困难问题之上,具有很高的安全强度。
文摘In this paper, we describe a hard-decision decoding technique based on Genetic Algorithms (HDGA), which is applicable to the general case of error correcting codes where the only known structure is given by the generating matrix G. Then we present a new soft-decision decoding based on HDGA and the Chase algorithm (SDGA). The performance of some binary and non-binary Linear Block Codes are given for HDGA and SDGA over Gaussian and Rayleigh channels. The performances show that the HDGA decoder has the same performances as the Berlekamp-Massey Algorithm (BMA) in various transmission channels. On the other hand, the performances of SDGA are equivalent to soft-decision decoding using Chase algorithm and BMA (Chase-BMA). The complexity of decoders proposed is also discussed and compared to those of other decoders.
基金Supported by the National Science and Technology Major Project of China(No.2013ZX03006004)
文摘In deep sub-micron ICs, growing amounts of on-die memory and scaling effects make embedded memories more vulnerable to reliability problems, such as soft errors induced by radiation. Error Correction Code(ECC) along with scrubbing is an efficient method for protecting memories against these errors. However, the latency of coding circuits brings speed penalties in high performance applications. This paper proposed a "bit bypassing" ECC protected memory by buffering the encoded data and adding an identifying address for the input data. The proposed memory design has been fabricated on a 130 nm CMOS process. According to the measurement, the proposed scheme only gives the minimum delay overhead of 22.6%, compared with other corresponding memories. Furthermore, heavy ion testing demonstrated the single event effects performance of the proposed memory achieves error rate reductions by 42.9 to 63.3 times.
文摘The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with heuristic techniques such as genetic algorithms and local search algorithms. In this paper we propose two approaches to attack the hardness of this problem. The first approach is based on genetic algorithms and it yield to good results comparing to another work based also on genetic algorithms. The second approach is based on a new randomized algorithm which we call 'Multiple Impulse Method (MIM)', where the principle is to search codewords locally around the all-zero codeword perturbed by a minimum level of noise, anticipating that the resultant nearest nonzero codewords will most likely contain the minimum Hamming-weight codeword whose Hamming weight is equal to the minimum distance of the linear code.
文摘In this paper we present an efficient algorithm to decode linear block codes on binary channels. The main idea consists in using a vote procedure in order to elaborate artificial reliabilities of the binary received word and to present the obtained real vector r as inputs of a SIHO decoder (Soft In/Hard Out). The goal of the latter is to try to find the closest codeword to r in terms of the Euclidean distance. A comparison of the proposed algorithm over the AWGN channel with the Majority logic decoder, Berlekamp-Massey, Bit Flipping, Hartman-Rudolf algorithms and others show that it is more efficient in terms of performance. The complexity of the proposed decoder depends on the weight of the error to decode, on the code structure and also on the used SIHO decoder.
