TITLE:      Encoding algorithms for complex approximations in Z[e^(2 pi i)/8]
AUTHORS:    M. W. Marcellin and T. R. Fischer
JOURNAL:    IEEE Transactions on Information Theory
ABSTRACT:
It has been shown [1,2] that the algebraic integers of the cyclotomic 
extension of the rationals Q(e^{2\pi i/n}), $n=2^\v, \v\ge 3$, yield 
approximations of complex numbers that are more suitable for residue 
number system computations than ordinary Gaussian integer approximations.  
This is due to the fact that the range requirement of the 
representation is greatly reduced. Algorithms for encoding arbitrary 
complex numbers into suitable algebraic integer approximations have been 
developed in [3].  Unfortunately these algorithms are computationally 
intense and may not be suitable for real time data encoding.  We present 
two computationally simple algorithms for encoding with n=8: one 
algorithm gives approximations within any desired error tolerance while 
providing a trade-off between range and memory requirements; the other 
algorithm satisfies the desired accuracy requirement with a relatively 
small memory requirement while making a small sacrifice in range.