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# Algorithm in Diagnostics of Signature Analysis

IP.com Disclosure Number: IPCOM000102208D
Original Publication Date: 1990-Nov-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 3 page(s) / 111K

IBM

## Related People

Chan, JC: AUTHOR [+1]

## Abstract

An algorithm is presented for fault diagnostics using information from the faulty signature. Likely fault locations are searched before any tests are performed, thereby reducing the number of tests required to diagnose the faults with the probability of error aliasing. Such probability is always smaller than that of error detection in signature analysis. When matching tests are difficult or impossible, this algorithm provides an estimate of where errors which caused the incorrect signature may have occurred.

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Algorithm in Diagnostics of Signature Analysis

An algorithm is presented for fault diagnostics using
information from the faulty signature.  Likely fault locations are
searched before any tests are performed, thereby reducing the number
of tests required to diagnose the faults with the probability of
error aliasing.  Such probability is always smaller than that of
error detection in signature analysis.  When matching tests are
difficult or impossible, this algorithm provides an estimate of where
errors which caused the incorrect signature may have occurred.

Notation and Theoretical Derivation: In conventional use, the
signature analyzer is first initialized, then the output response of
a circuit under test is serially compressed into a signature.  It is
well known that S = R(x) Mod G(x)

For our application in fault diagnosis, the following
information is known:
G(x),   Characteristic polynomial of the signature analyzer (degree
n).
S(x),   The correct signature generated from the response of a
fault-free circuit, S(x)=R mod G(x).
S'(x),  The signature generated from the response of a faulty
circuit, S'(x) = R' mod G(x).

If the output response of a fault-free circuit is R(x) which
generates the corresponding S(x), then the objective of the
diagnostic is to identify the bit locations to which R(x) and R'(x)
differed.

Let E(x) be an error polynomial in which each non-zero
coefficient represents an error in the corresponding bit position,
then the error sequence is the bit-wise Exclusive-OR of R and R'
where "E" is a unit vector of dimension 1m1, representing a single
bit error at the jth bit position that constitutes the ith error
polynomial "E". Thus, the error signature "Se" can be further
expanded as follows:
Se  =  S  + S' ;

In the expression above, the signature "Se" for multi-bit
errors is expanded in the form of a single-bit error sequence
signature.

The objective of the expansion in the diagnostic is to target
the search space of the fault locations once a faulty signature is
observed.   Given a signature analyzer with characteristic polynomial
of G(x), the corresponding set of "Si" can be computed easily and is
independent of the input sequence.  The computation can be
implemented in software, with G(x) and "m" as the only input
variables.

Application to Fault Diagnostic:

Assume "m" for the circuit under test is less than the vector
space of the signature analyzer.  In general, when a faulty signature
is observed, the reduction on the number of required tests is
achieved by targeting the search space of fault locations as follows:

First interpret the error signature "Se" as being due to single
bit error.  The fault location "j" is obtained by simply identifying
an...