SHAPE-ORIENTED TEST SET COMPRESSION METHOD USING IDEAL VECTOR SORTING AND SHAPES by James Chien-Chun Huang B.A.Sc. (Electrical and Computer Engineering), The University of British Columbia, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING We accept this thesis as conforming to the rennired standard THE UNIVERSITY OF BRITISH COLUMBIA March 2002 © James Chien-Chun Huang, 2002 UBC Special Collections - Thesis Authorisation Form Page 1 of 1 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of "SUtCTRIChL AAJQ CPM PlATBR FAJ6J /tyEE&ltyfy The University of British Columbia Vancouver, Canada Date HarcL 3-<P . ^QO^ http://www.library.ubc.ca/spcoll/mesauth.html 27/03/2002 ABSTRACT This thesis details a novel shape-oriented test set compression method that offers an alternative approach to reduce large test data of a complex circuit under test (CUT) such as the system-on-a-chip (SoC). Rather than the usual one-dimensional compression approach utilized by other contemporary compression techniques, such as the Huffman coding and Lempel-Ziv-Welch (LZW) method, the proposed method compresses a test set in a two-dimensional style. To achieve the compression, the proposed method initially sorts test cubes, which are sent to the combinational CUT to detect the single stuck-at faults of the chip, by employing the ideal vector sorting algorithm; the algorithm rearranges cubes based on the test data that resemble parts of predefined shapes identified in the cubes. After the cubes are sorted, the amalgamated-shapes area-covering algorithm of the proposed method attempts to discover predefined shapes or blocks and stores the corresponding information. In the last stage of the proposed method, the multi-syntax encoding algorithm converts the stored information into encoding bits. The experimental results show that the proposed method has higher compression ratios compared to that of other contemporary compression schemes in most cases. As a result, compared to other schemes, employing the shape-oriented method can lessen the time of transferring and can reduce the memory for storing the compressed data further. ii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iii LIST OF FIGURES vi LIST OF TABLES viii LIST OF ABBREVIATIONS x ACKNOWLEDGEMENTS xi DEDICATION xii 1 INTRODUCTION 1 2 VARIOUS CONTEMPORARY TEST DATA COMPRESSION METHODS.... 7 2.1 Run-Length Coding 7 2.2 Run-Length Coding and Burrows-Wheeler Transformation 8 2.3 Test Vector Decompression via Cyclical Scan Chain Architecture 10 2.4 Serial Scan Test Vector Compression Methodology 13 2.5 Differential Block Coding 14 2.6 Huffman Coding 16 2.7 Statistical Code Selection 17 2.8 Lempel-Ziv 77, Lempel-Ziv 78, and Lempel-Ziv-Welch 19 2.9 Test Width Compression Based on Counter Architecture 21 3 FORMER GEOMETRIC-PRIMITIVES-BASED COMPRESSION 23 3.1 Zero- or One-Distance Sorting Algorithm 25 3.1.1 Weights Assignment 26 3.1.2 Sorting Process 29 iii 3.2 Area-Covering Algorithm 32 3.3 Encoding Algorithm 32 3.4 The Advantage and Disadvantages of the Former Method 34 3.4.1 Advantage 34 3.4.2 Disadvantages 35 SHAPE-ORIENTED TEST SET COMPRESSION METHOD USING IDEAL VECTOR SORTING AND SHAPES 37 4.1 Ideal Vector Sorting Algorithm 39 4.1.1 Primary Window 41 4.1.2 Secondary Window 44 4.1.3 Ideal Vector Library 46 4.1.3.1 Values of Ideal Bits Stored in the Ideal Vector Library 47 4.1.3.2 Weight Assignments 48 4.1.4 Ideal Vector Sorting Process 52 4.2 Amalgamated-Shapes Area-Covering Algorithm 55 4.2.1 All-Zero or All-One Block 58 4.2.2 Primitive Shapes 58 4.2.3 Primitive Shape Extensions 59 4.2.4 Imperfect Triangle 60 4.2.5 Four-Bit by Four-Bit Blocks 64 4.2.6 Shape and Block Recognition Processes 66 4.2.6.1 Shape Recognition Process 66 4.2.6.2 Four-Bit by Four-Bit Block Recognition Process 71 4.2.7 Overall Area-Covering Algorithm 73 4.3 Multi-Syntax Encoding Algorithm 82 4.3.1 Distance Concept and Permanent Lengths of Encoding Sequences 83 iv 4.3.2 Original or Real Data Encoding Syntax 90 4.3.3 Four-Bit by Four-Bit Block Encoding Syntax 92 4.3.4 All-Zero or All-One Block Encoding Syntax 94 4.3.5 Primitive, Extended, and Imperfect Shapes Encoding Syntax 95 4.3.6 Overall Encoding Algorithm 101 4.4 Multi-Syntax Decoding Algorithm 103 4.5 Verification Processes 106 4.5.1 Sorted Test Data Verification 107 4.5.2 Decompressed Test Data Verification 109 4.6 Advantages and Disadvantages of the Shape-Oriented Compression Method. 110 4.6.1 Advantages 110 4.6.2 Disadvantages 112 5 EXPERIMENTAL RESULTS 114 5.1 Experimental Approach and Assumptions 114 5.2 Experimental Equipment 119 5.3 Cost of Test Set Compression 119 5.4 Experimental Results 120 5.4.1 Comparisons Among the Compression Methods 120 5.4.2 Miscellaneous Experimental Information 128 6 PROPOSALS FOR THE COURSES OF THE FUTURE RESEARCH 135 7 CONCLUSION 137 REFERENCES 139 APPENDIX A EXPERIMENTAL-RESULT ADDENDUM 143 v LIST OF FIGURES Number Page Figure 2.1 An Example of Modified 3-Bit Run-Length Code 12 Figure 3.1 Examples of Shapes (a) A Shape (b) A Primitive Shape - Triangle 24 Figure 3.2 Comparing Neighbouring Bits in the Distance Sorting Algorithm 27 Figure 3.3 An Example of Weight Calculation in Zero-Distance Sorting 28 Figure 3.4 The Flowchart of the Zero-Distance Sorting Algorithm 30 Figure 3.5 An Overview of the Encoding Algorithm Procedure of the Former Compression Method 33 Figure 4.1 The Concept of Employing an Ideal Vector 40 Figure 4.2 Primary Window and Its Corresponding Ideal Bit 41 Figure 4.3 Cases for Smaller Primary Window, (a) The Corresponding Ideal Bit is 1; (b) The Corresponding Ideal Bit is 0 42 Figure 4.4 Examples with Same Content in the Primary Window, (a) The Window with Original Dimension (b) The Enlarged Primary Window 43 Figure 4.5 The Secondary Windows With the Matching Primary Window 44 Figure .4.6 Different Configuration of Bits in the Secondary Windows Results a Different Ideal Bit 45 Figure 4.7 Examples of Weight Assignments from the Attribute - Number of Shapes. (a) An Example of Pattern Receives a Weight of 3; (b) A Pattern Receives a Weight of 0 49 Figure 4.8 Flowchart of the Ideal Vector Sorting Process 54 Figure 4.9 Four-Bit by Four-Bit Blocks in an 8-Bit by 8-Bit Partitioned Block 65 Figure 4.10 A Pseudo Code of Shape Recognition Process 69 Figure 4.11 An Example of Recognizing a Vertical Line 70 Figure 4.12 The Four Four-Bit by Four-Bit Blocks in an 8-Bit by 8-bit Partitioned Block 72 vi Figure 4.13 A Suggested Pseudo Code of a Four-Bit by Four-Bit Block Recognition Process 73 Figure 4.14 The Flowchart of the Overall Area Covering Algorithm 75-76 Figure 4.15 (a) The Positions of the Required Points (b) After the Modification, the Locations of the Required Points 87 Figure 4.16 A Pseudo Code of the Overall Encoding Algorithm 102 Figure 4.17 A Pseudo Code of the Overall Decoding Algorithm 104 Figure 4.18 Relationships Between Verification Procedures and Compression and Decompression Algorithms 107 Figure 4.19 A Pseudo Code of the Sorted Test Data Verification 108 Figure 4.20 A Pseudo Code of the Decompressed Test Data Verification 109 Figure 5.1 The Relationship Among Pins, Cubes, and Compression Ratio 129 Figure 5.2 Correlation Between Percentages of Zeros and Compression Ratios 130 Figure 5.3 Correlation Between Percentages of Ones and Compression Ratios 131 Figure 5.4 Correlation Between Percentages of Don't Cares and Compression Ratios 131 Figure 5.5 Distributions of Blocks and Shapes of Former and Proposed Methods 133 vn LIST OF TABLES Number Page Table 3.1 Table of Zero-Distance Weights 27 Table 3.2 Table of One-Distance Weights 28 Table 4.1 Weight Assignment Table for the Pattern Attribute - Number of Shapes .... 49 Table 4.2 Weight Assignment Table for the Pattern Attribute - Continuity of the Bits in Two Sorted Cubes 50 Table 4.3 Weight Assignment Table for the Pattern Attribute - Degree of Certainty of the Value of an Ideal Bit 51 Table 4.4 Table of Shapes Utilized in the Proposed Area-Covering Process 56 Table 4.5 Legitimate Alternatives of Each Imperfect Triangle Variation 62 Table 4.6 An Intuitive Approach of Storing Information Regarding a Triangle 84 Table 4.7 Relationships Among the Coordinates of Primitive Triangles in Table 4.6.. 86 Table 4.8 Relationships Among the Coordinates of a Primitive Rectangle in Figure 4.15 (a) 87 Table 4.9 Encoding Table (Category Header) of Real or Original Data Block 91 Table 4.10 Encoding Table (Block Information) of Real or Original Data Block 91 Table 4.11 Encoding Table (Category Header) of the Four-Bit by Four-Bit Block 92 Table 4.12 Encoding Table (Block Information) of the Four-Bit by Four-Bit Block 93 Table 4.13 Encoding Table (Category Header) of the All-Zero/All-One Block 94 Table 4.14 Encoding Table (Block Information) of the All-Zero/All-One Block 95 Table 4.15 Encoding Table (Category Header) of the Block Represented by Shapes ...