VLSI Architectures for multidimensional fourier transform processing
IEEE Transactions on Computers
Optimal VLSI circuits for sorting
Journal of the ACM (JACM)
Optimal VLSI architectures for multidimensional DFT
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
VLSI Architectures for Multidimensional Transforms
IEEE Transactions on Computers
Parallel Implementation of Multidimensional Transforms without Interprocessor Communication
IEEE Transactions on Computers
The Area-Time Complexity of Binary Multiplication
Journal of the ACM (JACM)
Information transfer and area-time tradeoffs for VLSI multiplication
Communications of the ACM
AT2L2 o N2/2 for fast fourier transform in multilayer VLSI
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Optimal VLSI Networks for Multidimensional Transforms
IEEE Transactions on Parallel and Distributed Systems
The Influence of Key Length on the Area-Time Complexity of Sorting
Proceedings of the 12th Colloquium on Automata, Languages and Programming
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
A complexity theory for VLSI
Computational Aspects of VLSI
A method for computation of the discrete Fourier transform over a finite field
Problems of Information Transmission
A Combinatorial Limit to the Computing Power of VLSI Circuits
IEEE Transactions on Computers
The Discrete Fourier Transform Over Finite Rings with Application to Fast Convolution
IEEE Transactions on Computers
IEEE Transactions on Computers
Algebraic theory of finite fourier transforms
Journal of Computer and System Sciences
A fast algorithm for the Fourier transform over finite fields and its VLSI implementation
IEEE Journal on Selected Areas in Communications
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Area-time lower bounds are derived for the VLSI computation of the (n1 X n2 X... X nd)-point multidimensional DFT (MDDFT) over different types of rings and different types of input/output protocols. First, an AT2 = Ω ((N log |R|)2) bound is obtained for any finite ring R, where N = Πdk=1 nk, for any word-local protocol. The bound was previously known for the special case when R = ZM, the ring of integers modulo M. Second, an AT2 = Ω ((Nb)2) word-local bound is derived when R is the complex field, the components of the input are fixed-point numbers of b bits, and the precision of the output components guarantees that the resulting approximate transform is injective. No area-time lower bound was previously known for the DFT over the complex field. Third, an AT2 = Ω ((N log |R|)2) bound is derived when R = GF (pm) is a finite field of polynomials of degree m with coefficients in Zp, for certain classes of non word-local protocols. This is the first area-time lower bound derived for the DFT with I/O protocols that are not word-local.