On the polynomial residue number system [digital signal processing]

The theory of the polynomial residue number system (PRNS), a system in which totally parallel polynomial multiplication can be achieved provided that the arithmetic takes place in some carefully chosen ring, is examined. Such a system is defined by a mapping which maps the problem of multiplication of two polynomials onto a completely parallel scheme where the mapped polynomial coefficients are multiplied pairwise. The properties of the mapping and the rules of operations in the PRNS are proven. Choices of the rings for which the PRNS is defined are also studied. It is concluded that the PRNS can offer significant advantages in those digital signal processing (DSP) applications that involve multiplication-intensive algorithms like convolutions and one-dimensional or multidimensional correlation