On the equivalence between Berlekamp's and Euclid's algorithms
IEEE Transactions on Information Theory
On the VLSI Design of a Pipeline Reed-Solomon Decoder Using Systolic Arrays
IEEE Transactions on Computers
On the high-speed VLSI implementation of errors-and-erasures correcting reed-solomon decoders
Proceedings of the 12th ACM Great Lakes symposium on VLSI
High-speed architectures for Reed-Solomon decoders
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
A VLSI Design of a Pipeline Reed-Solomon Decoder
IEEE Transactions on Computers
On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding
IEEE Transactions on Information Theory
An area-efficient VLSI architecture of a Reed-Solomon decoder/encoder for digital VCRs
IEEE Transactions on Consumer Electronics
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The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the iterations in the EEA are stopped when the degree of the remainder polynomial falls below a threshold. While determining the degree of a polynomial is a simple task for human beings, hardware implementation of this stopping rule is more complicated. This paper describes a modified version of the EEA that is specifically adapted to the RS decoding problem. This modified algorithm requires no degree computation or comparison to a threshold, and it uses a fixed number of iterations. Another advantage of this modified version is in its application to the errors-and-erasures decoding problem for RS codes where significant hardware savings can be achieved via seamless computation.