Array processors using a quadratic residue number system

Abstract

Algorithms and architectures are described for optical matrix-matrix and matrix-vector processing. Implementations are based on quadratic residue number system coding which has the remarkable property that computations in the real and imaginary channels are performed in parallel without any interactions. This approach significantly reduces the complexity of implementation. Residue-based processing provides increased dynamic range and a reduced number of computations with high speed and parallelism of the optics fully utilized. Several architectures of optical processors described in this paper include systolic and data flow arrays.

Optical complex-valued modular multiplication based on digital partitioning and weighting shifting

“…Our experimental result is shown in Figure 3; the three center lines correspond to the mixed negabinary values of convolution results in Eq. (10). Both sides (top and bottom) of these three lines have an additional six lines, corresponding to those unwanted convolutions, which will be discussed in future research reports.…”

“…but the result in the output is bit reversed to the mixed negabinary values in Eq. (10). Considering the inverse imaging function of the positive lens optical system, this point can be well understood.…”