Fault tolerant Fermat Number Transform domain adaptive filters based on modulus replication RNS architectures

In previous work it was shown that a combination of Fermat Number Transform (FNT) domain block processing and polynomial ring theory provides computationally efficient fault tolerance for adaptive filters implemented in highly scaled nanotechnology circuits. Since the FNT requires finite field integer arithmetic it is compatible with Modulus Replication RNS (MRRNS) arithmetic that has powerful error detection/correction capabilities as well as the potential for low power realizations. This paper proposes a hybrid combination of Fermat Number Transform block processing and MRRNS coding that can be used to realize adaptive filters that are immune to a wide range of transient and hard errors.