Design of common sub expression elimination algorithm in fast Fourier transform

Common sub expression elimination (CSE) is a critical procedure in many multiplierless implementations of DSP algorithms. The aim of CSE is dual-pronged to reduce the number of logic operators used and to minimize the logic depth (critical path) of the DSP algorithm implemented in VLSI. CSE algorithm combines greedy algorithm and exhaustive search to select the best set of common sub expressions is proposed. Using CSE algorithm, we reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs) requiring fewer additions.

[1]  Ning Chen,et al.  High-performance designs of AES transformations , 2009, 2009 IEEE International Symposium on Circuits and Systems.

[2]  Sandro Bellini,et al.  On the Reduction of Additive Complexity of Cyclotomic FFTs , 2012, IEEE Transactions on Communications.

[3]  Mou Ling Dennis Wong,et al.  A new common subexpression elimination algorithm with application in composite field AES S-box , 2010, 10th International Conference on Information Science, Signal Processing and their Applications (ISSPA 2010).

[4]  Peter Trifonov,et al.  Finding roots of polynomials over finite fields , 2002, IEEE Trans. Commun..

[5]  Trieu-Kien Truong,et al.  Fast algorithm for computing the roots of error locator polynomials up to degree 11 in Reed-Solomon decoders , 2001, IEEE Trans. Commun..

[6]  Patrick Schaumont,et al.  A new algorithm for elimination of common subexpressions , 1999, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[7]  Peter Trifonov,et al.  A Method for Fast Computation of the Fourier Transform over a Finite Field , 2003, Probl. Inf. Transm..

[8]  Sandro Bellini,et al.  On the Structure of Cyclotomic Fourier Transforms and Their Applications to Reed-Solomon Codes , 2011, IEEE Transactions on Communications.

[9]  Ning Chen,et al.  Cyclotomic FFTs With Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm , 2007, IEEE Transactions on Signal Processing.