Summary: Draft of 16 Apr 2003 3:30 a.m.
The Guruswam-Sudan Decoding Algorithm for Reed-Solomon Codes.
R. J. McEliece
Abstract: This paper is a tutorial discussion of the Guruswami-Sudan Reed-Solomon de-
coding algorithm, including self-contained treatments of the KĻotter and Roth-Ruckenstein
improvements. It also contains a number of new results, including a rigorous discussion of
the average size of the decoder's list, an improvement in the RR algorithm's stopping rule,
a simplified treatment of the combinatorics of weighted monomial orders, and a proof of
the monotonicity of the GS decoding radius as a function of the interpolation multiplicity.
Table of Contents:
Section 1. Introduction.
Section 2. A First Look at the Guruswami-Sudan Algorithm.
Section 3. Polynomials in Two Variables I: Monomial Orders and Generalized Degree.
Section 4. Polynomials in Two Variables II: Zeros and Multiple Zeros.
Section 5. The Interpolation and Factorization Theorems.
Section 6. A Second Look at the Guruswami-Sudan Algorithm.
Section 7. KĻotter's Solution to the Interpolation Problem.
Section 8. An Alternative to KĻotter's Solution: The Feng-Tzeng Algorithm.
Section 9. The Roth-Ruckenstein Solution to the Factorization Problem.
Section 10. Appendix: The Function F(x) and the Numbers Km.