An analysis of the aliasing probability of multiple-input signature registers in the case of a 2m-ary symmetric channel

The aliasing probabilities of multiple-input signature registers (MISR) with m inputs for a 2^m-ary symmetric channel, where each of the (2^m-1) possible errors is equally likely, are analyzed. For this error model, the aliasing probabilities of MISRs are analyzed using the weight distributions of maximum-distance-separable (MDS) codes. The results show that the aliasing probabilities over the 2^m-ary symmetric channel do not depend on the polynomials that characterize the MISRs. That is, for the 2^m-ary symmetric channel, the aliasing probability of an MISR based on a primitive polynomial is exactly the same as one based on a nonprimitive one. In addition, it is observed that the aliasing probabilities, P_al (n), as a function of test length n, are monotonous for error probabilities p=0.2, 0.4, and 0.8. The aliasing probabilities of multiple MISRs based on Reed-Solomon codes are analyzed again for the 2^m -ary symmetric channel, using the weight distributions of Reed-Solomon codes, which are MDS codes