High-speed, low-complexity systolic designs of novel iterative division algorithms in GF(2/sup m/)

We extend the binary algorithm invented by Stein and propose novel iterative division algorithms over GF(2/sup m/) for systolic VLSI realization. While algorithm EBg is a basic prototype with guaranteed convergence in at most 2m - 1 iterations, its variants, algorithms EBd and EBdf, are designed for...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. 53; no. 3; pp. 375 - 380
Main Authors: Wu, Chien-Hsing, Wu, Chien-Ming, Shieh, Ming-Der, Hwang, Yin-Tsung
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2004
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Digital arithmetic
Galois fields
Systolic arrays
Very-large-scale integration
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:We extend the binary algorithm invented by Stein and propose novel iterative division algorithms over GF(2/sup m/) for systolic VLSI realization. While algorithm EBg is a basic prototype with guaranteed convergence in at most 2m - 1 iterations, its variants, algorithms EBd and EBdf, are designed for reduced complexity and fixed critical path delay, respectively. We show that algorithms EBd and EBdf can be mapped to parallel-in parallel-out systolic circuits with low area-time complexities of O(m/sup 2/loglogm) and O(m/sup 2/), respectively. Compared to the systolic designs based on the extended Euclid's algorithm, our circuits exhibit significant speed and area advantages.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2004.1261843