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Polynomial modular multipliers for error correcting code devices  

Authors
 Poperechny P.S.
Date of publication
 2016

Abstract
 It is known that, the widespread and complicated arithmetic operation in error correction coding is a multiplying. In spite of being the formal derivative, dividing, power operations in RS-codes, all of these operations are collapsed to adding and multiplying in extended Galois Field. Once decided of data length, all vector multiplying are performed by the one primitive polynomial that generates Field. So it is very hard to change this polynomial in work circuit. The proposed approach allows changing primitive polynomial. The calculation ďforgetsĒ original extension of Field, thatís why itís very easy to return to any Field after calculation just by means of primitive polynomial dividing. Even more, as input vectors are imaged to residue polynomials, all calculations are shared by parallel small calculating block. These blocks have so small critic path delay, and common performance throughput is increased.
Keywords
 Error-correction coding, extended Galois Field, primitive polynomial, polynomial multiplier, residue number system, SoC.
Library reference
 Poperechny P.S. Polynomial modular multipliers for error correcting code devices // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2016. Proceedings / edited by A. Stempkovsky, Moscow, IPPM RAS, 2016. Part1. P. 274-277.
URL of paper
 http://www.mes-conference.ru/data/year2016/pdf/D009.pdf

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