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On Modulus Replication for Residue Arithmetic Computations of Complex Inner Products
August 1990 (vol. 39 no. 8)
pp. 1065-1076

A technique is presented for coding weighted magnitude components (e.g. bits) of numbers directly into polynomial residue rings, such that repeated use may be made of the same set of moduli to effectively increase the dynamic range of the computation. This effectively limits the requirement for large sets of relatively prime moduli, For practical computations over quadratic residue rings, at least 6-bit moduli have to be considered. It is shown that 5-bit moduli can be effectively used for large dynamic range computations.

[1] N. S. Szabo and R. I. Tanaka,Residue Arithmetic and Its Applications to Computer Technology. New York: McGraw-Hill. 1967.
[2] M. A. Soderstrand, W. K. Jenkins, G. A. Jullien, and F. J. Taylor, Eds.,Modern Applications of Residue Number System Arithmetic to Digital Signal Processing. New York: IEEE Press, 1986.
[3] J. M. Pollard, "The fast Fourier transform in a finite field,"Math. Computat., vol. 25, pp. 365-374, Apr. 1971.
[4] W. K. Jenkins and J. V. Krogmeier, "The design of dual-mode complex signal processors based on quadratic modular number codes,"IEEE Trans. Circuits Syst., (invited paper), vol. CAS-34, no. 4, pp. 354-364, Apr. 1987.
[5] G. A. Jullien, P. D. Bird, J. R. Carr, M. Taheri, and W. C. Miller, "An efficient bit-level systolic cell design for finite ring digital signal processing applications,"J. VLSI Signal Processing, 1989.
[6] N. Wigley and G. A. Jullien, "Encoding integers into direct product representations of finite polynomial rings,"IEEE Trans. Inform. Theory, submitted for publication.
[7] T. Stouraitis and A. Skavantzos, "Parallel decomposition of complex multipliers," inProc. 22d. Asilomar Conf. Circuit Syst. Comput., Dec. 1988, pp. 379-383.
[8] M. Taheri, G. A. Jullien, and W. C. Miller, "High speed signal processing using systolic arrays over finite rings,"IEEE Trans. Select. Areas Commun., VLSI in Communications III, vol. 6, no. 3, pp. 504-512, Apr. 1988.
[9] G. A. Jullien, "Residue number scaling and other operations using ROM arrays,"IEEE Trans. Comput., vol. C-27, pp. 325-336, Apr. 1978.
[10] A. P. Senoy and R. Kumaresan, "Residue to binary conversion for RNS arithmetic using only modular look-up tables," Submitted toIEEE Trans. Circuits Syst.

Index Terms:
modulus replication; residue arithmetic computations; complex inner products; coding; weighted magnitude components; bits; polynomial residue rings; quadratic residue rings; 6-bit moduli; 5-bit moduli; dynamic range computations; decoding; digital arithmetic; number theory.
Citation:
N.M. Wigley, G.A. Jullien, "On Modulus Replication for Residue Arithmetic Computations of Complex Inner Products," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1065-1076, Aug. 1990, doi:10.1109/12.57045
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