Parallel signature analyzers using hybrid design of their linear feedbacks

A bottom-top exclusive OR (BTE) type multiple input linear feedback shift register (MISR) and a top-bottom exclusive OR (TBE) type MISR which use only (t+1)/2 XOR gates in their linear feedback are presented. An algebraic analysis of the operation and certain analytical results regarding the detection capability of a BTE MISR are included. Infirmities of certain BTE type MISRs and TBE type MISRs with a reducible characteristic polynomial have been made. The proof that the probability of error sequence aliasing on a single input of BTE or TBE type MISR, where a characteristic polynomial of degree n is reducible, asymptotically approaches a value greater or equal to 2^-n is also given