Optical complex-valued modular multiplication based on digital partitioning

摘要

Abstract: In this paper, we presented a scheme for complex-valued modular multiplication based on digital partitioning technique. The module ($MIN@2)$+N$/-1 is introduced for its simple arithmetic. Both of the operands joining in the complex number multiplication are treated as two N-bit real numbers. Because of its advantage in expressing number, the negabinary number system is adopted. The subtraction in complex number multiplication is converted to addition operation by weighting shifting. Although the direct result takes the looks of a serial of residues, we proposed an algorithm for reconstructing the complex-valued multiplication produce by studying the product decomposing rules. The algorithm can be implemented in parallel manner, we studied the optical implementation based on an incoherent optical correlator and some electronic devices as auxiliary for reconstructing the product. Both the advantage and the disadvantage are analyzed. And the comparison with other optical complex-valued multiplication algorithms is also presented.!18