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A Universal Reed-Solomon Decoder
IBM Journal of Research and Development, 1984Summary: Two architectures for universal Reed-Solomon decoders are given. These decoders, called time-domain decoders, work directly on the raw data word as received without the usual syndrome calculation or power-sum-symmetric functions. Up to the limitations of the working registers, the decoders can decode any Reed-Solomon codeword or BCH codeword ...
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On decoding of Reed-Solomon codes
IEEE Transactions on Information Theory, 1971It is shown how nonsystematic Reed-Solomon (RS) codes encoded by means of the Chinese remainder theorem can be decoded using the Berlekamp algorithm. The Chien search and calculation of error values are not needed but are replaced by a polynomial division and added calculation in determining the syndrome.
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A parametrical architecture for Reed-Solomon decoders
Proceedings of the Sixth Great Lakes Symposium on VLSI, 2002Reed-Solomon decoders are digital decoders that use RS detecting and correcting of errors codes. RS codes are widely diffused in the transmission and storage of digital information and they are often used in concatenated encoding schemes to obtain great correction capabilities and good robustness to burst errors.
M. Petre, MASERA, Guido
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Proceedings of the IEEE 1999 Custom Integrated Circuits Conference (Cat. No.99CH36327), 2003
Reed-Solomon (RS) codes are used in many of today's communications systems. RS codes use finite field arithmetic which DSPs don't implement efficiently. In previous RS hardware designs, a unique hardware solution was designed for each system. In this paper we describe a single hardware design which is programmable.
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Reed-Solomon (RS) codes are used in many of today's communications systems. RS codes use finite field arithmetic which DSPs don't implement efficiently. In previous RS hardware designs, a unique hardware solution was designed for each system. In this paper we describe a single hardware design which is programmable.
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A systolic Reed-Solomon encoder
IEEE Transactions on Information Theory, 1991An architecture for a Reed-Solomon (RS) encoder is presented, consisting of r+1 systolic cells, where r is the redundancy of the code. The systolic encoder is systematic, does not contain any feedback or other global signals, its systolic cells are of low complexity, and it is easily reconfigurable for variable redundancy and changes in the choice of ...
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1999
In December of 1958 I. S. Reed and G. Solomon finished the report, entitled “polynomial codes over certain finite fields” at the M.I.T Lincoln Laboratory [1]. In 1960, a slight modification of this report was published as a paper [2] in the Journal of the Society for Industrial and Applied Mathematics(SIAM).
Irving S. Reed, Xuemin Chen
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In December of 1958 I. S. Reed and G. Solomon finished the report, entitled “polynomial codes over certain finite fields” at the M.I.T Lincoln Laboratory [1]. In 1960, a slight modification of this report was published as a paper [2] in the Journal of the Society for Industrial and Applied Mathematics(SIAM).
Irving S. Reed, Xuemin Chen
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1994
The purpose of this chapter is to give an overview of Reed-Solomon (RS) codes [67] as an important subclass of nonbinary Bose-Chaudhuri-Hocquenghem (BCH) codes. Our aim is in this chapter to cover the background which is required for the forthcoming sections related to RS codes.
S. Hamidreza Jamali, Tho Le-Ngoc
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The purpose of this chapter is to give an overview of Reed-Solomon (RS) codes [67] as an important subclass of nonbinary Bose-Chaudhuri-Hocquenghem (BCH) codes. Our aim is in this chapter to cover the background which is required for the forthcoming sections related to RS codes.
S. Hamidreza Jamali, Tho Le-Ngoc
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Chinese Annals of Mathematics, Series B, 2010
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. This two-part paper addresses this problem. In the first part, the author improves known upper bounds for the error distance of a received word to a Reed-Solomon code over \(\text{GF}(q)\).
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The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. This two-part paper addresses this problem. In the first part, the author improves known upper bounds for the error distance of a received word to a Reed-Solomon code over \(\text{GF}(q)\).
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2019
In this chapter, we will give information about Reed-Solomon codes. These codes fall into the category of nonbinary cyclic codes. The generator polynomials of Reed-Solomon codes are constructed using the minimal polynomials of the extended finite fields. Reed-Solomon codes are effective for burst errors and they are used for erasure decoding.
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In this chapter, we will give information about Reed-Solomon codes. These codes fall into the category of nonbinary cyclic codes. The generator polynomials of Reed-Solomon codes are constructed using the minimal polynomials of the extended finite fields. Reed-Solomon codes are effective for burst errors and they are used for erasure decoding.
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2001
So far, we’ve looked at bit-oriented error correcting schemes. Reed-Solomon (RS) codes, however, are symbol-based. In other words, bits are combined into symbols upon which the coding is performed. RS codes are a special example of a more general class of block codes called BCH codes after Bose, Chaudhuri and Hocquenghem, forefathers of the theory ...
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So far, we’ve looked at bit-oriented error correcting schemes. Reed-Solomon (RS) codes, however, are symbol-based. In other words, bits are combined into symbols upon which the coding is performed. RS codes are a special example of a more general class of block codes called BCH codes after Bose, Chaudhuri and Hocquenghem, forefathers of the theory ...
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