
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
ChihWei Liu, KuoTai Huang, ChungChin Lu, "A Systolic Array Implementation of the FengRao Algorithm," IEEE Transactions on Computers, vol. 48, no. 7, pp. 690706, July, 1999.  
BibTex  x  
@article{ 10.1109/12.780877, author = {ChihWei Liu and KuoTai Huang and ChungChin Lu}, title = {A Systolic Array Implementation of the FengRao Algorithm}, journal ={IEEE Transactions on Computers}, volume = {48}, number = {7}, issn = {00189340}, year = {1999}, pages = {690706}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.780877}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  A Systolic Array Implementation of the FengRao Algorithm IS  7 SN  00189340 SP690 EP706 EPD  690706 A1  ChihWei Liu, A1  KuoTai Huang, A1  ChungChin Lu, PY  1999 KW  Errorcorrecting codes KW  algebraicgeometric codes KW  FengRao algorithm KW  systolic array. VL  48 JA  IEEE Transactions on Computers ER   
Abstract—An efficient implementation of a parallel version of the FengRao algorithm on a onedimensional systolic array is presented in this paper by adopting an extended syndrome matrix. Syndromes of the same order, lying on a slant diagonal in the extended syndrome matrix, are scheduled to be examined by a series of cells simultaneously and, therefore, a high degree of concurrency of the FengRao algorithm can be achieved. The time complexity of the proposed architecture is
[1] V.D. Goppa, “Codes Associated with Divisors,” Probl. Peredachi Inform., vol. 13, no. 1, pp. 3339, 1977.
[2] V.D. Goppa, “Codes on Algebraic Curves,” Dokl. Akad. Nauk SSSR, vol. 24, pp. 170172, 1981.
[3] V.D. Goppa, “AlgebraicGeometric Codes,” Izv. Akad. Nauk. SSSR, vol. 21, pp. 7591, 1983.
[4] M.A. Tsfasman, S.G. Vladut, and T. Zink, “Modular Curves, Shimura Curves, and Goppa Codes Better Than VarshamoveGilbert Bound,” Math. Nachr., vol. 104, pp. 1328, 1982.
[5] G.D. Forney Jr., “On Decoding BCH Codes,” IEEE Trans. Information Theory, vol. 11, pp. 549557, Oct. 1965.
[6] E.R. Berlekamp, Algebraic Coding Theory. New York: McGrawHill, 1968.
[7] J. Massey,“Shiftregister synthesis and BCH decoding,” IEEE Trans. on Information Theory, vol. 15, pp. 122127, 1969.
[8] S. Sakata, “Highly Concurrent Parallel Version of the BerlekampMassey Algorithm and Its Pipelined Architecture,” Proc. ISITA '94, pp. 1,0691,072, Sydney, Australia, 1994.
[9] F.J. MacWilliams and N.J.A. Sloane, The Theory of ErrorCorrecting Codes. New York: NorthHolland, 1978.
[10] H. Stichtenoth, Algebraic Function Fields and Codes. New York: SpringerVerlag, 1993.
[11] M.A. Tsfasman and S.G. Vladut, “Geometric Approach to Higher Weights,” IEEE Trans. Information Theory, vol. 41, pp. 15,641,588, Nov. 1995.
[12] T. Høholdt and R. Pellikaan, “On the Decoding of AlgebraicGeometric Codes,” IEEE Trans. Information Theory, vol. 41, pp. 1,5891,614, Nov. 1995.
[13] J. Justesen, K.J. Larsen, H.E. Jensen, A. Havemose, and T. Høholdt, “Construction and Decoding of a Class of Algebraic Geometry Codes,” IEEE Trans. Information Theory, vol. 35, pp. 811821, May 1989.
[14] G.L. Feng and T.R.N. Rao, “Decoding AlgebraicGeometric Codes Up to the Designed Minimum Distance,” IEEE Trans. Information Theory, vol. 39, pp. 3745, Jan. 1993.
[15] G. Strang, Linear Algebra and Its Applications, third ed. San Diego, Calif.: Harcourt Brace Jova novich, 1988.
[16] W. Fulton, Algebraic Curves. New York: W.A. Benjamin, 1969.
[17] G.L. Feng, V.K. Wei, T.R.N. Rao, and K.K. Tzeng, “Simplified Understanding and Effect Decoding of a Class of AlgebraicGeometric Codes,” IEEE Trans. Information Theory, vol. 40, pp. 9811,002, July 1994.
[18] K. Saints and C. Heegard, “AlgebraicGeometric Codes and Multidimensional Cyclic Codes: A Unified Theory and Algorithms for Decoding Using Gröbner Bases,” IEEE Trans. Information Theory, vol. 41, pp. 1,7331,751, Nov. 1995.
[19] S. Sakata, J. Justesen, Y. Madelung, H.E. Jensen, and T. Hohøldt, “A Fast Decoding Method of AG Codes from MiuraKamiya Curves$C_{ab}$Up to Half the FengRao Bound,” Finite Fields and Their Applications, vol. 1, pp. 83101, 1995.
[20] M. Kurihara and S. Sakata, “A Fast Parallel Decoding Algorithm for General OnePoint AG Codes with a Systolic Array Architecture,” Proc. IEEE ISIT '95, p. 99, 1995.
[21] S. Sakata and M. Kurihara, “A Systolic Array Architecture for Implementation a Fast Parallel Decoding Algorithm of OnePoint AG Codes,” Proc. IEEE ISIT '97, p. 378, 1997.
[22] M.E. O'Sullivan, “VLSI Architecture for a Decoder for Hermitian Codes,” Proc. IEEE ISIT '97, p. 376, 1997.
[23] R. Kötter, “Fast Generalized MinimumDistance Decoding of AlgebraicGeometry and ReedSolomon Codes,” IEEE Trans. Information Theory, vol. 42, pp. 721737, May 1996.
[24] A. Skorobogatov and S. Vladut, “On the Decoding of AlgebraicGeometric Codes,” IEEE Trans. Information Theory, vol. 36, pp. 1,0511,060, Sept. 1990.
[25] H.T. Kung, “Why Systolic Architectures?,” Computer, vol. 15, no. 1, pp. 3746, Jan. 1982.
[26] S.Y. Kung, VLSI Array Processors. Prentice Hall, 1988.
[27] P.S. Tseng, A Systolic Array Parallelizing Compiler. Boston: Kluwer Academic, 1990.
[28] B. Hochet,P. Quinton, and Y. Robert,"Systolic Gaussian Elimination overGF(p) with Partial Pivoting," IEEE Trans. Computers, vol. 38, no. 9, pp. 1,3211,324, Sept. 1989.
[29] G.L. Feng and T.R.N. Rao, “A Simple Approach for Construction of AlgebraicGeometric Codes from Affine Plane Curves,” IEEE Trans. Information Theory, vol. 40, pp. 1,0031,012, July 1994.