A modified Guruswami-Sudan algorithm for decoding Reed-Solomon codes

We tighten a key estimate, which dictates the computational complexity of Guruswami-Sudan algorithm, on the lower bound of the degrees of freedom, and then propose a modified decoding algorithm for Reed-Solomon codes beyond half the minimum distance. The computational complexity of the modified algorithm is lower than the Guruswami-Sudan algorithm for the medium to high rate Reed-Solomon codes, and has the same asymptotic complexity as the algorithm proposed by Wu. Besides we also claim that our modified algorithm outperforms Wu's algorithm to some extent.

[1]  Yingquan Wu,et al.  New List Decoding Algorithms for Reed–Solomon and BCH Codes , 2007, IEEE Transactions on Information Theory.

[2]  Alexander Vardy,et al.  Algebraic soft-decision decoding of Reed-Solomon codes , 2003, IEEE Trans. Inf. Theory.

[3]  Shuhong Gao,et al.  Computing Roots of Polynomials over Function Fields of Curves , 1999 .

[4]  Shuhong Gao,et al.  A New Algorithm for Decoding Reed-Solomon Codes , 2003 .

[5]  Alexander Vardy,et al.  Divide-and-conquer interpolation for list decoding of reed-solomon codes , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[6]  Selmer M. Johnson.  A new upper bound for error-correcting codes , 1962, IRE Trans. Inf. Theory.

[7]  R. Roth,et al.  Efficient decoding of Reed-Solomon codes beyond half the minimum distance , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[8]  Venkatesan Guruswami,et al.  Improved decoding of Reed-Solomon and algebraic-geometry codes , 1999, IEEE Trans. Inf. Theory.

[9]  Elwyn R. Berlekamp,et al.  Algebraic coding theory , 1984, McGraw-Hill series in systems science.

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

[11]  Madhu Sudan,et al.  Decoding of Reed Solomon Codes beyond the Error-Correction Bound , 1997, J. Complex..

[12]  V. Wei,et al.  Error-Correcting Codes for List Decoding , 1994 .

[13]  R. Kotter.  Fast generalized minimum-distance decoding of algebraic-geometry and Reed-Solomon codes , 1996 .

[14]  Alexander Barg,et al.  Performance Analysis of Algebraic Soft-Decision Decoding of Reed–Solomon Codes , 2008, IEEE Transactions on Information Theory.

[15]  R. McEliece.  The Guruswami-Sudan Decoding Algorithm for Reed-Solomon Codes , 2003 .

[16]  Alexander Vardy,et al.  A complexity reducing transformation in algebraic list decoding of Reed-Solomon codes , 2003, Proceedings 2003 IEEE Information Theory Workshop (Cat. No.03EX674).

[17]  Vijay K. Bhargava.  Communications, Information and Network Security , 2010 .