A simple derivation of the Berlekamp- Massey algorithm and some applications

Another viewpoint is presented on the derivation of the Berlekamp-Massey algorithm. Our approach differs from previous ones in the following manner. The properties of the shortest linear feedback shift register that generates a given sequence are first derived Without reference to the Berlekamp-Massey algorithm. The Berlekamp-Massey algorithm is then derived using these properties. Our approach has the advantage of being easier to understand.

[1]  N J Sloane,et al.  Codes for multiplex spectrometry. , 1969, Applied optics.

[2]  N. J. A. Sloane,et al.  Voronoi regions of lattices, second moments of polytopes, and quantization , 1982, IEEE Trans. Inf. Theory.

[3]  Toby Berger,et al.  Permutation codes for sources , 1972, IEEE Trans. Inf. Theory.

[4]  Masao Kasahara,et al.  A Method for Solving Key Equation for Decoding Goppa Codes , 1975, Inf. Control..

[5]  Dilip V. Sarwate,et al.  Decoding of Alternant Codes , 1976 .

[6]  M. R. Schroeder,et al.  Adaptive predictive coding of speech signals , 1970, Bell Syst. Tech. J..

[7]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[8]  Chin-Long Chen,et al.  High-speed decoding of BCH codes , 1981, IEEE Trans. Inf. Theory.

[9]  D. Slepian.  Permutation Modulation , 1965, Encyclopedia of Wireless Networks.

[10]  Hermann J. Helgert.  Decoding of alternant codes (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[11]  Manfred R. Schroeder,et al.  Rate distortion theory and predictive coding , 1981, ICASSP.