STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Guessing secrets efficiently via list decoding
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Scalable secure storage when half the system is faulty
Information and Computation
On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Scalable Secure Storage when Half the System Is Faulty
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
List Decoding from Erasures: Bounds and Code Constructions
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
Efficient Traitor Tracing Algorithms Using List Decoding
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Linear time encodable and list decodable codes
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Towards a VLSI Architecture for Interpolation-Based Soft-Decision Reed-Solomon Decoders
Journal of VLSI Signal Processing Systems
Fast factorization architecture in soft-decision Reed-Solomon decoding
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Partial parallel factorization in soft-decision Reed-Solomon decoding
GLSVLSI '06 Proceedings of the 16th ACM Great Lakes symposium on VLSI
High-speed interpolation architecture for soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Guessing secrets efficiently via list decoding
ACM Transactions on Algorithms (TALG)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low-latency factorization architecture for algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A Syndrome Formulation of the Interpolation Step in the Guruswami-Sudan Algorithm
ICMCTA '08 Proceedings of the 2nd international Castle meeting on Coding Theory and Applications
Soft-decision list decoding of hermitian codes
IEEE Transactions on Communications
Key equations for list decoding of Reed-Solomon codes and how to solve them
Journal of Symbolic Computation
M-ary hyper phase-shift keying with Reed Solomon encoding and soft decision reliability information
MILCOM'09 Proceedings of the 28th IEEE conference on Military communications
A modified Guruswami-Sudan algorithm for decoding Reed-Solomon codes
Information Processing Letters
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Algebraic soft-decision decoder architectures for long Reed-Solomon codes
IEEE Transactions on Circuits and Systems II: Express Briefs
List decoding of generalized reed-solomon codes by using a modified extended key equation algorithm
EURASIP Journal on Wireless Communications and Networking
The decoding Library for list decoding
ACM Communications in Computer Algebra
Near-Optimal collusion-secure fingerprinting codes for efficiently tracing illegal re-distribution
CSS'12 Proceedings of the 4th international conference on Cyberspace Safety and Security
A minimal search soft decision list decoding algorithm for Reed-Solomon codes
International Journal of Information and Communication Technology
| Hi-index | 754.96 |
A list decoding algorithm is presented for [n,k] Reed-Solomon (RS) codes over GF(q), which is capable of correcting more than [(n-k)/2] errors. Based on a previous work of Sudan (see J. Compl., vol.13, p.180-93, 1997), an extended key equation (EKE) is derived for RS codes, which reduces to the classical key equation when the number of errors is limited to [(n-k)/2]. Generalizing Massey's (1969) algorithm that finds the shortest recurrence that generates a given sequence, an algorithm is obtained for solving the EKE in time complexity O(l·(n-k)2 ), where l is a design parameter, typically a small constant, which s an upper bound on the size of the list of decoded codewords. (The case l=1 corresponds to classical decoding of up to [(n-k)/2] errors where the decoding ends with at most one codeword.) This improves on the time complexity O(n3) needed for solving the equations of Sudan's algorithm by a naive Gaussian elimination. The polynomials found by solving the EKE are then used for reconstructing the codewords in time complexity O((llog2l)k(n+llogq)) using root-finders of degree-l univariate polynomials