A divisionless form of the Schur Berlekamp-Massey algorithm

  • Christopher J. Zarowski
Coding and Cryptography
Part of the Lecture Notes in Computer Science book series (LNCS, volume 793)


A procedure exists for mapping the Berlekamp-Massey algorithm (BMA) into so-called Schur form. This procedure will be shown here to be applicable to the development of a divisionless Schur BMA. When the BMA is combined with the Schur BMA the result is an efficient parallel algorithm for the computation of the error-locator polynomial which is used in the decoding of Reed-Solomon, or, more generally, Bose-Chaudhuri-Hocquenghem codes.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    C. J. Zarowski, ”Schur Algorithms for Hermitian Toeplitz, and Hankel Matrices with Singular Leading Principal Submatrices,” IEEE Trans. on Signal Proc., vol. 39, Nov. 1991, pp. 2464–2480.Google Scholar
  2. [2]
    H.-M. Zhang, P. Duhamel, ”On the Methods for Solving Yule-Walker Equations,” IEEE Trans. on Signal Proc., vol. 40, Dec. 1992, pp. 2987–3000.Google Scholar
  3. [3]
    S.-Y. Kung, Y. H. Hu, ”A Highly Concurrent Algorithm and Pipelined Architecture for Solving Toeplitz Systems,” IEEE Trans. on Acoust., Speech, and Signal Proc., vol. ASSP-31, Feb. 1983, pp. 66–75.Google Scholar
  4. [4]
    C. J. Zarowski, ”Parallel Implementation of the Schur Berlekamp-Massey Algorithm on a Linearly Connected Processor Array,” to appear in the IEEE Transactions on Computers (accepted September 1993).Google Scholar
  5. [5]
    X. Youzhi, ”Implementation of Berlekamp-Massey Algorithm Without Inversion,” IEE Proc.-I, vol. 138, June 1991, pp. 138–140.Google Scholar
  6. [6]
    R. Blahut, Theory and Practice of Error Control Codes. Reading, Massachusetts: Addison-Wesley, 1983.Google Scholar
  7. [7]
    T. Citron, ”Algorithms and Architectures for Error Correcting Codes,” Ph. D. dissertation, Stanford University, 1986.Google Scholar
  8. [8]
    R. Blahut, ”A Universal Reed-Solomon Decoder,” IBM J. Res. Dev., vol. 28, Mar. 1984, pp. 150–158.Google Scholar
  9. [9]
    Y. Shayan, T. Le-Ngoc, V. Bhargava, ”A Versatile Time-Domain Reed-Solomon Decoder,” IEEE J. on Sel. Areas in Comm., vol. 8, Oct. 1990, pp. 1535–1542.Google Scholar
  10. [10]
    H. M. Shao, I. S. Reed, ”On the VLSI Design of a Pipeline Reed-Solomon Decoder Using Systolic Arrays,” IEEE Trans. on Comp., vol. 37, Oct. 1988, pp. 1273–1280.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Christopher J. Zarowski
    • 1
  1. 1.Department of Electrical EngineeringQueen's UniversityKingstonCanada

Personalised recommendations