Isomorphic transformation and its application to the modulo (2n + 1) channel for RNS based FIR filter design

Abstract

In this paper, the implementation of a Finite Impulse Response (FIR) filter in the Residue Number System (RNS), is presented, in which a modulo multiplier based on the isomorphism technique is used to perform multiplication in the ( 2 n + 1 ) channel. An RNS modular multiplication in the Galois Field GF ( 2 n + 1 ) is presented in detail in this paper. The multiplication is based on the isomorphic mapping technique adapted to the residue arithmetic. The isomorphic encoder and decoder look-up tables in the GF ( 2 8 + 1 ) are given. An architecture for FIR filter design based on distributed arithmetic for multiplication and accumulation in mentioned ( 2 n + 1 ) channel is also presented. This architecture is discussed in details and compared with with architecture based on isomorphing technique.