A combinatorial approach to X-tolerant compaction circuits

TL;DR

This paper presents a combinatorial framework for designing X-tolerant circuit compaction techniques that effectively detect errors despite unknown logic values, improving test efficiency in scan-based IC testing.

Contribution

It introduces a new combinatorial model for X-codes, develops novel design methods, and provides existence theorems for optimal X-compactors with high error detection capabilities.

Findings

Developed a combinatorial model for X-compact design

Established nonconstructive existence theorems for optimal X-compactors

Proposed design techniques for X-codes with small fan-out

Abstract

Test response compaction for integrated circuits (ICs) with scan-based design-for-testability (DFT) support in the presence of unknown logic values (Xs) is investigated from a combinatorial viewpoint. The theoretical foundations of X-codes, employed in an X-tolerant compaction technique called X-compact, are examined. Through the formulation of a combinatorial model of X-compact, novel design techniques are developed for X-codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values, while requiring only small fan-out. The special class of X-codes that results leads to an avoidance problem for configurations in combinatorial designs. General design methods and nonconstructive existence theorems to estimate the compaction ratio of an optimal X-compactor are also derived.