Decoding algebraic-geometric codes beyond the error-correction bound
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Chinese remaindering with errors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A displacement approach to efficient decoding of algebraic-geometric codes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Coding Constructions for Blacklisting Problems without Computational Assumptions
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Towards a VLSI Architecture for Interpolation-Based Soft-Decision Reed-Solomon Decoders
Journal of VLSI Signal Processing Systems
A hybrid list decoding and chase-like algorithm of Reed-Solomon codes
WISICT '05 Proceedings of the 4th international symposium on Information and communication technologies
A displacement approach to decoding algebraic codes
Contemporary mathematics
Decoding interleaved Reed-Solomon codes over noisy channels
Theoretical Computer Science
Efficient Reed-Solomon Iterative Decoder Using Galois Field Instruction Set
SAMOS '08 Proceedings of the 8th international workshop on Embedded Computer Systems: Architectures, Modeling, and Simulation
Decoding of interleaved Reed Solomon codes over noisy data
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Hi-index | 754.84 |
We present a new Reed-Solomon decoding algorithm, which embodies several refinements of an earlier algorithm. Some portions of this new decoding algorithm operate on symbols of length lgq bits; other portions operate on somewhat longer symbols. In the worst case, the total number of calculations required by the new decoding algorithm is proportional to nr, where n is the code's block length and r is its redundancy. This worst case workload is very similar to prior algorithms. But in many applications, average-case workload and error-correcting performance are both much better. The input to the new algorithm consists of n received symbols from GF(q), and n nonnegative real numbers, each of which is the reliability of the corresponding received symbol. Any conceivable errata pattern has a “score” equal to the sum of the reliabilities of its locations with nonzero errata values. A max-likelihood decoder would find the minimum score over all possible errata patterns. Our new decoding algorithm finds the minimum score only over a subset of these possible errata patterns. The errata within any candidate errata pattern may be partitioned into “errors” and “erasures,” depending on whether the corresponding reliabilities are above or below an “erasure threshold.” Different candidate errata patterns may have different thresholds, each chosen to minimize its corresponding ERRATA COUNT, which is defined as 2·(number of errors)+(number of erasures). The new algorithm finds an errata pattern with minimum score among all errata patterns for which ERRATA COUNT⩽r+1 where r is the redundancy of the RS code. Conventional algorithms also require that the erasure threshold be set a priori; the new algorithm obtains the best answer over all possible settings of the erasure threshold. Conventional cyclic RS codes have length n=q-1, and their locations correspond to the nonzero elements of GF(q). The new algorithm also applies very naturally to RS codes which have been doubly extended by the inclusion of 0 and ∞ as additional locations