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
This paper provides a fast algorithm for Grobner bases of homogenous ideals of F[x, y] over a finite field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite homogenours generating s...This paper provides a fast algorithm for Grobner bases of homogenous ideals of F[x, y] over a finite field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite homogenours generating set are needed in the computing of a Grobner base of the homogenous ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. We also show that the computational complexity of our new algorithm is O(N2), where N is the maximum degree of the input generating polynomials. The new algorithm can be used to solve a problem of blind recognition of convolutional codes. This problem is a new generalization of the important problem of synthesis of a linear recurring sequence.展开更多
This paper provides a fast algorithm for Grobnerbases of homogenous ideals of F[x, y] over a finite field F. We show that only the 8-polynomials of neighbor pairs of a strictly ordered finite homogenours generating se...This paper provides a fast algorithm for Grobnerbases of homogenous ideals of F[x, y] over a finite field F. We show that only the 8-polynomials of neighbor pairs of a strictly ordered finite homogenours generating set are needed in the computing of a Grobner base of the homogenous ideal. It reduces dramatically the number of unnecessary 5-polynomials that are processed. We also show that the computational complexity of our new algorithm is O（N^2）, where N is the maximum degree of the input generating polynomials. The new algorithm can be used to solve a problem of blind recognition of convolutional codes. This problem is a new generalization of the important problem of synthesis of a linear recurring sequence.展开更多
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.
基金the National Natural Science Foundation of China (Grant Nos. 10471091, 10671027)Foundation of Shanghai Education Committee (Grant No. 06FZ029)"One Hundred Talents Program" from University of Science and Technology of China
文摘This paper provides a fast algorithm for Grobner bases of homogenous ideals of F[x, y] over a finite field F. We show that only the S-polynomials of neighbor pairs of a strictly ordered finite homogenours generating set are needed in the computing of a Grobner base of the homogenous ideal. It reduces dramatically the number of unnecessary S-polynomials that are processed. We also show that the computational complexity of our new algorithm is O(N2), where N is the maximum degree of the input generating polynomials. The new algorithm can be used to solve a problem of blind recognition of convolutional codes. This problem is a new generalization of the important problem of synthesis of a linear recurring sequence.
基金the National Natural Science Foundation of China (Grant No. 60673082)Special Funds of Authors of Excellent Doctoral Dissertation in China (Grant No. 200084)
文摘This paper provides a fast algorithm for Grobnerbases of homogenous ideals of F[x, y] over a finite field F. We show that only the 8-polynomials of neighbor pairs of a strictly ordered finite homogenours generating set are needed in the computing of a Grobner base of the homogenous ideal. It reduces dramatically the number of unnecessary 5-polynomials that are processed. We also show that the computational complexity of our new algorithm is O（N^2）, where N is the maximum degree of the input generating polynomials. The new algorithm can be used to solve a problem of blind recognition of convolutional codes. This problem is a new generalization of the important problem of synthesis of a linear recurring sequence.
