On the Use of an Algebraic Signature Analyzer for Mixed-Signal Systems Testing

Abstract

We propose an approach to design of an algebraic signature analyzer that can be used for mixed-signal systems testing. The analyzer does not contain carry propagating circuitry, which improves its performance as well as fault tolerance. The common design technique of a signature analyzer for mixed-signal systems is based on the rules of an arithmetic finite field. The application of this technique to the systems with an arbitrary radix is a challenging task and the devices designed possess high hardware complexity. The proposed technique is simple and applicable to systems of any size and radix. The hardware complexity is low. The technique can also be used in arithmetic/algebraic coding and cryptography.

On the Theory and Design of Polynomial Division Circuits

“…This circuit is an r-stage shift register with no feedbacks. The remainder (28) only depends on the last r symbols of the sequence of k 2 m -ary symbols. Since r k, only a small portion of all possible errors in the sequence is detected.…”

“…Proof: The proof becomes evident if take into consideration the fact that the maximum value for g is 2 mr − 1. Indeed, if we select the higher modulus (yet available with the m-bit bus), g = 2 mr = b r , then, similarly to (28),…”

“…If the range was contiguous, we could use a window comparator (that only requires two signatures, lower and upper ones) to verify that the actual signature drops into the range. One solution to make the range contiguous is to rearrange the set of reference signatures [28]. Another solution is the use of any arithmetic signature analyzers examined in section 4.1.…”