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1 Complexity of Decoding PositiveRate Primitive ReedSolomon Codes
"... Abstract—It has been proved that the maximum likelihood decoding problem of ReedSolomon codes is NPhard. However, the length of the code in the proof is at most polylogarithmic in the size of the alphabet. For the complexity of maximum likelihood decoding of the primitive ReedSolomon code, whose ..."
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Abstract—It has been proved that the maximum likelihood decoding problem of ReedSolomon codes is NPhard. However, the length of the code in the proof is at most polylogarithmic in the size of the alphabet. For the complexity of maximum likelihood decoding of the primitive ReedSolomon code, whose
Complexity of Decoding PositiveRate ReedSolomon Codes
"... Abstract. The complexity of maximum likelihood decoding of the ReedSolomon codes [q − 1, k]q is a well known open problem. The only known result [4] in this direction states that it is at least as hard as the discrete logarithm in some cases where the information rate unfortunately goes to zero. In ..."
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Cited by 4 (3 self)
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. In this paper, we remove the rate restriction and prove that the same complexity result holds for any positive information rate. In particular, this resolves an open problem left in [4], and rules out the possibility of a polynomial time algorithm for maximum likelihood decoding problem of ReedSolomon codes
ReedSolomon Encoder and Decoder
"... ABSTRACT (Continue on reverse aide II neceeaary and Identity by block number) A systolic array is a natural architecture for the implementation of a ReedSolomon (RS) encoder and decoder. It possesses many of the properties desired for a specialpurpose application: simple and regular design, concur ..."
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ABSTRACT (Continue on reverse aide II neceeaary and Identity by block number) A systolic array is a natural architecture for the implementation of a ReedSolomon (RS) encoder and decoder. It possesses many of the properties desired for a specialpurpose application: simple and regular design
Improved Decoding of ReedSolomon and AlgebraicGeometry Codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon codes ..."
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Cited by 343 (42 self)
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Given an errorcorrecting code over strings of length n and an arbitrary input string also of length n, the list decoding problem is that of finding all codewords within a specified Hamming distance from the input string. We present an improved list decoding algorithm for decoding ReedSolomon
ReedSolomon Codes by
"... class of errorcorrecting codes that are now called ReedSolomon (RS) codes. These codes have great power and utility, and are today found in many ..."
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class of errorcorrecting codes that are now called ReedSolomon (RS) codes. These codes have great power and utility, and are today found in many
Limits to list decoding ReedSolomon codes
 STOC’05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, 602–609, ACM
, 2005
"... In this paper, we prove the following two results that expose some combinatorial limitations to list decoding ReedSolomon codes. 1. Given n distinct elements α1,..., αn from a field F, and n subsets S1,..., Sn of F each of size at most ℓ, the list decoding algorithm of Guruswami and Sudan [7] can i ..."
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Cited by 10 (3 self)
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In this paper, we prove the following two results that expose some combinatorial limitations to list decoding ReedSolomon codes. 1. Given n distinct elements α1,..., αn from a field F, and n subsets S1,..., Sn of F each of size at most ℓ, the list decoding algorithm of Guruswami and Sudan [7] can
The GuruswamiSudan Decoding Algorithm for ReedSolomon Codes
, 2003
"... This article is a tutorial discussion of the GuruswamiSudan (GS) ReedSolomon decoding algorithm, including selfcontained treatments of the Kotter and Roth Ruckenstein (RR) improvements. It also contains a number of new results, including a rigorous discussion of the average size of the decode ..."
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This article is a tutorial discussion of the GuruswamiSudan (GS) ReedSolomon decoding algorithm, including selfcontained treatments of the Kotter and Roth Ruckenstein (RR) improvements. It also contains a number of new results, including a rigorous discussion of the average size
Subspace subcodes of ReedSolomon codes
, 1995
"... Abstract — In this paper we introduce a class of nonlinear cyclic errorcorrecting codes, which we call subspace subcodes of Reed–Solomon (SSRS) codes. An SSRS code is a subset of a parent Reed–Solomon (RS) code consisting of the RS codewords whose components all lie in a fixeddimensional vector su ..."
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Cited by 8 (0 self)
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dimension than any previously known code with the same values of n; d; and q; including algebraicgeometry codes. These examples suggest that highrate SSRS codes are promising candidates to replace Reed–Solomon codes in highperformance transmission and storage systems. Index Terms—Errorcorrecting codes
with ReedSolomon constituent codes 1
, 2009
"... Low density parity check codes on bipartite graphs ..."
150 A Universal ReedSolomon Decoder
"... Two architecturesfor universal ReedSolomon decoders are given. These decoders, called timedomain decoders, work directly on the raw data word as received without the usual syndrome calculation or powersumsymmetric functions Up to the limitations of the working registers, the decoders can decode ..."
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any ReedSolomon codeword or BCH codeword in the presence of both errors and erasures. Provision is also made for decoding extended codes and shortened codes.
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