OPTICAL COMPLEX-VALUED MODULAR MULTIPLICATION BASED ON DIGITAL PARTITIONING AND WEIGHTING SHIFTING.

In this Letter we propose complex modular multiplication of two N-bit negabinary complex numbers by adopting digital partitioning and weighting-shifting techniques. The module (-2)^N - 1 is introduced for its simple arithmetic. Both complex numbers are treated as two N-bit negabinary real numbers. All four real numbers are decomposed into several short bytes; a corresponding complex product modular (-2)^N - 1 is achieved by cyclic convolution. The subtraction in complex multiplication is converted to addition by weighting shifting. The algorithms can be implemented in a fully parallel manner, especially for optics. Both pre- and postprocessing are simple. The proof-of-principle experiment is performed by an incoherent optical correlator, and results are given. [ABSTRACT FROM AUTHOR]