The Multipolynomial Channel

The residue number system (RNS) is an integer system appropriate for implementing fast digital signal processors since it can support parallel carry-free high-speed arithmetic. A recent development in residue arithmetic is the polynomial RNS (PRNS) which can perform a polynomial product modulo ( ) with only multiplications instead of , provided that arithmetic takes place in appropriate modular rings. The PRNS, however, has one major limitation in that the sizes of the modular rings used for the PRNS arithmetic are proportional to the size of the polynomials to be multiplied. As a result, if large polynomials need to be multiplied, large modular rings must be chosen, a fact which can imply severe performance degradation of the entire system. In this paper, a solution to the major limitation of the PRNS is offered. The solution is the multipolynomial channel PRNS, which is capable of performing large polynomial products requiring large dynamic ranges with arithmetic performed in many small modular rings. This way, very high-speed internal PRNS processing is ensured.

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