Fault tolerant design of signed digit based FIR filters

This paper proposes a methodology for the development of fault tolerant arithmetic circuits using an r-radix signed digit (SD) representation. A residue checking based technique is applied to detect errors caused by faults belonging to the considered stuck-at fault set. We developed a technique to detect the presence of a fault in the adder by using a completely independent circuit that uses check symbols that are residues of the numbers modulo a suitable base. We show that for any radix r > 3 the correctness of the adder operation can be checked simply by using two check symbols. This property is used to extend the fault detection also to SD constant multipliers and to the rounding operation. The extension to SD constant multiplier can be easily obtained by implementing the multipliers using a shift and add architecture. For the truncation operation we notice that many error detection techniques based on some arithmetic properties of the circuits fails when the truncation operation is performed. Instead, we show how our method can be applied to this operation with low area overhead and therefore it is useful to implement self-checking finite impulse response (FIR) filters