Cyclotomic FFTs with reduced additive complexities based on a novel common subexpression elimination algorithm

Authors:
Ning Chen;Zhiyuan Yan
Affiliations:
Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA;Department of Electrical and Computer Engineering, Lehigh University, Bethlehem, PA
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 10
Cited 1

The fast Fourier transform and its applications

The fast Fourier transform and its applications
Error control systems for digital communication and storage

Error control systems for digital communication and storage
Mastrovito Multiplier for All Trinomials

IEEE Transactions on Computers
The Design and Analysis of Computer Algorithms

The Design and Analysis of Computer Algorithms
A Method for Fast Computation of the Fourier Transform over a Finite Field

Problems of Information Transmission
A method for computation of the discrete Fourier transform over a finite field

Problems of Information Transmission
Fast, prime factor, discrete Fourier transform algorithms over GF(2m) for 8≤m≤10

Information Sciences: an International Journal
Multiple constant multiplications: efficient and versatile framework and algorithms for exploring common subexpression elimination

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A new algorithm for elimination of common subexpressions

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A New Common Subexpression Elimination Algorithm for Realizing Low-Complexity Higher Order Digital Filters

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Additive fast Fourier transforms over finite fields

IEEE Transactions on Information Theory

Quantified Score

Hi-index	35.74

Visualization

Abstract

In this paper, we first propose a novel common subexpression elimination (CSE) algorithm for matrix-vector multiplications over characteristic-2 fields. As opposed to previously proposed CSE algorithms, which usually focus on complexity savings due to recurrences of subexpressions, our CSE algorithm achieves two types of complexity reductions, differential savings and recurrence savings, by taking advantage of the cancelation property of characteristic-2 fields. Using our CSE algorithm, we reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs). Using a weighted sum of the numbers of multiplications and additions as a metric, our CFFTs achieve smaller total complexities than previously proposed CFFTs and other FFTs, requiring both fewer multiplications and fewer additions in many cases.