Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rat...Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.展开更多
In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obta...In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.展开更多
This paper presents a new Hard-Input Hard-Output (HIHO) iterative decoding algorithm for Turbo Product Codes (TPC), and especially describes the BCH-TPC codes aiming to alleviate error propagation and lower error floo...This paper presents a new Hard-Input Hard-Output (HIHO) iterative decoding algorithm for Turbo Product Codes (TPC), and especially describes the BCH-TPC codes aiming to alleviate error propagation and lower error floor. This algorithm mainly emp hasizes a decision mechanism for bit-flips, which thoroughly evaluates four different aspects of the decoding process, properly weighs and combines their respective reliability measures, and then employs the combined measure to make a judgment with regard to whether any particular bit should be flipped or not. Simulations result in a very steep Bit Error Rate (BER) curve indicating that a high-level net coding gain can be expected with a reasonable complexity. The simplicity and effectiveness of this HIHO decoding algorithm makes it a p romising candidate for the application in future high-speed fiber optical communications.展开更多
Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of...Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.展开更多
A novel product code iterative decoding algorithm and its high speed implementation scheme are proposed in this paper. Based on partial combination of selected columns of check matrix, the reduced-complexity syndrome ...A novel product code iterative decoding algorithm and its high speed implementation scheme are proposed in this paper. Based on partial combination of selected columns of check matrix, the reduced-complexity syndrome decoding method is proposed to decode sub-codes of product code and deliver soft output information. So iterative decoding of product codes is possible. The fast sorting algorithm and a look-up method are proposed for high speed implementation of this algorithm. Compared to the conventional weighing iterative algorithm, the proposed algorithm has lower complexity while offering better performance, which is demonstrated by simulations and implementation analysis. The implementation scheme and verilog HDL simulation show that it is feasible to achieve high speed decoding with the proposed algorithm.展开更多
The component codes of turbo product codes in WiMAX systems are extended Hamming codes and single parity check codes as well as their shortened forms, In this paper, three novel iterative decoding algorithms based on ...The component codes of turbo product codes in WiMAX systems are extended Hamming codes and single parity check codes as well as their shortened forms, In this paper, three novel iterative decoding algorithms based on Chase, MAP algorithms and their combination are proposed for shortened-extended turbo product codes. The iterative decoding algorithm based on Chase algorithm is proposed to reduce the decoding complexity without any performance loss. An efficient MAP algorithm is then proposed to decode the component codes of shortened single parity check codes and shortened-extended Hamming codes. A comprehensive performance comparison of the proposed decoding schemes is conducted for three typical classes of turbo product codes in WiMAX OFDMA systems. The suitable decoding algorithms are recommended for different classes based on the simulation results.展开更多
Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser&...Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser's curiosity increases to know about the production process which can be accomplished by production traceability system.The traceability system can store and superintend the specific attribute information about products regarding the productive centre,producer and production finish data.The products undergo various circulation processes and they are being managed by individually constructed traceability system.Thus,it is difficult for the producer and the consumer to guarantee the safety from transpirable issues about the falsification of production traceability because the traceability information can be re-produced by forging through various ways.So in this paper,we proposed a system for integrated management of agro-fishery products based on quick response code(QR-code)for forgery prevention which may help to solve these issues.The proposed system makes QR-code using production information provided by producer.And then it is provided to the distributor and the consumer through integrated service model using the QR-code.Therefore,this system make sure to provide the same production traceability about the products to the distributor and the consumer and always keeps both updated with the same information.展开更多
In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner pro...In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.展开更多
基金This work was supported in part by National Natural Science Foundation of China(No.61671324)the Director’s Funding from Pilot National Laboratory for Marine Science and Technology(Qingdao)(QNLM201712).
文摘Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.
文摘In this article, the Rosenbloom-Tsfasman metric of matrix product codes over finite commutative rings is studied and the lower bounds for the minimal Rosenbloom- Tsfasman distances of the matrix product codes axe obtained. The lower bounds of the dual codes of matrix product codes over finite commutative Frobenius rings are also given.
基金The authors would like to thank the editor and reviewer for helpful comments on the manuscripts. We also thank for the form support from Huawei Technology Corporations in this research. This work was partially supported by the National Natural Science Foundation of China under Grant No. 61101092.
文摘This paper presents a new Hard-Input Hard-Output (HIHO) iterative decoding algorithm for Turbo Product Codes (TPC), and especially describes the BCH-TPC codes aiming to alleviate error propagation and lower error floor. This algorithm mainly emp hasizes a decision mechanism for bit-flips, which thoroughly evaluates four different aspects of the decoding process, properly weighs and combines their respective reliability measures, and then employs the combined measure to make a judgment with regard to whether any particular bit should be flipped or not. Simulations result in a very steep Bit Error Rate (BER) curve indicating that a high-level net coding gain can be expected with a reasonable complexity. The simplicity and effectiveness of this HIHO decoding algorithm makes it a p romising candidate for the application in future high-speed fiber optical communications.
基金Supported by the National Aeronautical Foundation of Science and Research of China (No.04F52041)the Natural Science Foundation of Jiangsu Province (No.BK2006188).
文摘Low-Density Parity-Check (LDPC) code is one of the most exciting topics among the coding theory community.It is of great importance in both theory and practical communications over noisy channels.The most advantage of LDPC codes is their relatively lower decoding complexity compared with turbo codes,while the disadvantage is its higher encoding complexity.In this paper,a new ap- proach is first proposed to construct high performance irregular systematic LDPC codes based on sparse generator matrix,which can significantly reduce the encoding complexity under the same de- coding complexity as that of regular or irregular LDPC codes defined by traditional sparse parity-check matrix.Then,the proposed generator-based systematic irregular LDPC codes are adopted as con- stituent block codes in rows and columns to design a new kind of product codes family,which also can be interpreted as irregular LDPC codes characterized by graph and thus decoded iteratively.Finally, the performance of the generator-based LDPC codes and the resultant product codes is investigated over an Additive White Gaussian Noise (AWGN) and also compared with the conventional LDPC codes under the same conditions of decoding complexity and channel noise.
基金the National Natural Science Foundation of China.
文摘A novel product code iterative decoding algorithm and its high speed implementation scheme are proposed in this paper. Based on partial combination of selected columns of check matrix, the reduced-complexity syndrome decoding method is proposed to decode sub-codes of product code and deliver soft output information. So iterative decoding of product codes is possible. The fast sorting algorithm and a look-up method are proposed for high speed implementation of this algorithm. Compared to the conventional weighing iterative algorithm, the proposed algorithm has lower complexity while offering better performance, which is demonstrated by simulations and implementation analysis. The implementation scheme and verilog HDL simulation show that it is feasible to achieve high speed decoding with the proposed algorithm.
基金Supported by the National Natural Science Foundation of China (Grant No. 50534060)the National High-Tech Research & Development Program of China (Grant No. 2007AA01Z259)+1 种基金the Open Research Fund of National Mobile Communications Research Laboratory, South-east University (Grant No. W200816)State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications (Grant No. SKLNST-2008-1-11)
文摘The component codes of turbo product codes in WiMAX systems are extended Hamming codes and single parity check codes as well as their shortened forms, In this paper, three novel iterative decoding algorithms based on Chase, MAP algorithms and their combination are proposed for shortened-extended turbo product codes. The iterative decoding algorithm based on Chase algorithm is proposed to reduce the decoding complexity without any performance loss. An efficient MAP algorithm is then proposed to decode the component codes of shortened single parity check codes and shortened-extended Hamming codes. A comprehensive performance comparison of the proposed decoding schemes is conducted for three typical classes of turbo product codes in WiMAX OFDMA systems. The suitable decoding algorithms are recommended for different classes based on the simulation results.
基金The MSIP(Ministry of Science,ICT&Future Planning),Korea,under the ITRC(Information Technology Research Center)support program(NIPA-2013-H0301-13-2006)supervised by the NIPA(National IT Industry Promotion Agency)
文摘Recently,both the importance and awareness relating to food safety relating to agrochemicals,chemical fertilizers,the pollution of ecosystem and unwholesome foods are growing rapidly.For the same reason,the purchaser's curiosity increases to know about the production process which can be accomplished by production traceability system.The traceability system can store and superintend the specific attribute information about products regarding the productive centre,producer and production finish data.The products undergo various circulation processes and they are being managed by individually constructed traceability system.Thus,it is difficult for the producer and the consumer to guarantee the safety from transpirable issues about the falsification of production traceability because the traceability information can be re-produced by forging through various ways.So in this paper,we proposed a system for integrated management of agro-fishery products based on quick response code(QR-code)for forgery prevention which may help to solve these issues.The proposed system makes QR-code using production information provided by producer.And then it is provided to the distributor and the consumer through integrated service model using the QR-code.Therefore,this system make sure to provide the same production traceability about the products to the distributor and the consumer and always keeps both updated with the same information.
文摘In this paper, we discuss a kind of Hermitian inner product - symplectic inner product, which is different from the original inner product - Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others.
