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Combinatorial Group Testing Methods for the BIST Diagnosis Problem. Andrew B. Kahng. Sherief Reda. CSE & ECE Departments University of CA, San Diego La Jolla, CA 92093 [email protected]. CSE Department University of CA, San Diego La Jolla, CA 92093 [email protected]. - PowerPoint PPT Presentation
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Combinatorial Group Testing Methods for the BIST Diagnosis
Problem
Andrew B. Kahng Sherief RedaCSE & ECE Departments
University of CA, San DiegoLa Jolla, CA [email protected]
CSE DepartmentUniversity of CA, San Diego
La Jolla, CA [email protected]
Presented by Prof. C. K. ChengCSE Department
University of CA, San DiegoLa Jolla, CA [email protected]
UCSD VLSI CAD Laboratory, http://vlsicad.ucsd.edu
Outline
→ Diagnosis in BIST Environments
→ Combinatorial Group Testing (CGT)
→ New Diagnosis Techniques:─ Digging─ Multi-Stage Batching─ Doubling and Jumping─ Hybrid Techniques: Batched Binary Search
→ Experimental Results and Conclusions
Diagnosis in BIST Environments
Sca
n C
hain
Circuit Under Test
Compactor
Generator
1
00
0
11
01
0
1
10
0
110
0
0110
1
00
0
11
1
11
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00
Signature
A test session applies a number of test patterns
Sca
n C
hain
Circuit Under Test
Compactor
Generator
1
00
0
11
01
0
1
10
0
110
0
0110
1
00
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11
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10
1
00
fault
0
1Signature
A test session applies a number of test patterns
Diagnosis in BIST Environments
Problem: Given a faulty BIST environment, identify faulty scan cells (= subset of scan cells receiving faulty responses) in the minimum amount of time.
Abstractly: Given a set of items (scan cells), some of which are faulty (faulty scan cells), identify the subset of faulty items using a tester (compactor) that gives only a Yes/No response.
Diagnosis in BIST Environments
Diagnosis in BIST Environments
→ Combinatorial Group Testing (CGT)
→ New Diagnosis Techniques:─ Digging─ Multi-Stage Batching─ Doubling and Jumping─ Hybrid Techniques: Batched Binary Search
→ Experimental Results and Conclusions
Outline
Combinatorial Group Testing (CGT)
CGT tests groups of items instead of individual items. A group tests positive (faulty) when at least one item in the group tests positive.
CGT = Generic class of algorithms applied when many individuals or items are subjected to same test.
A CGT experiment consists of (1) defining the groups, and (2) a diagnosis or decoding procedure to infer the status of items from the status of groups.
We use CGT methods to improve existing diagnosis techniques, and as the basis of new techniques.
Diagnosis in BIST Environments
Combinatorial Group Testing (CGT)
→ New Diagnosis Techniques:─ Digging─ Multi-Stage Batching─ Doubling and Jumping─ Hybrid Techniques: Batched Binary Search
→ Experimental Results and Conclusions
Outline
New Diagnosis Techniques: Digging
Saves lots of diagnosis time with small number of faulty cells
1
2 7
1 2 3 4 5 6 7 8
3 986
10 1154
3 4 5 6 7 8
6
87
109
Binary Search Digging
Example: Digging saves one test session over Binary Search
Faulty Signature Fault-Free Signature
New Diagnosis Techniques: Multi-Stage Batching
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
STAGE 1
5 6 7 8 13 14 15 16
8 13 145 6 7 15 16
STAGE 2
8 13 14
8 13 14
STAGE 3
8 13
8 13
STAGE 4
Cell status undetermined
Faulty CellFault-Free cell
Saves lots of diagnosis time with large number of faulty cells
Divide scan cells under test into groups of size = square root of total.
New Diagnosis Techniques: Doubling
The number of faults is unknown
Cell status undetermined
Faulty cellFault-Free cell
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
11 2 32 3 4̀ 5 6 74̀ 5 6 7 8̀ 9 10 11 1̀2 13 14 15
8̀ 9 10 11 1̀2 13 14 15
Identify faulty cells using binary search
11 13
New Diagnosis Techniques: Hybrid Techniques
13 14 15 16
Phase 2: Binary Search or Digging
5 6 7 8
8 13
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 2 3 4 5 6 7 8 9 10 11 12
Phase 1: Batching
13 14 15 16
Diagnosis in BIST Environments
Combinatorial Group Testing (CGT) New Diagnosis Techniques:
─ Digging─ Multi-Stage Batching─ Doubling and Jumping─ Hybrid Techniques: Batched Binary Search
→ Experimental Results and Conclusions
Outline
Experimental Results
Faults Diagnosis Literature Proposed from CGT
Newly Proposed
A B C D E F G H I
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9
10
84
100
113
128
137
152
161
174
183
198
62
90
97
111
122
130
139
146
161
169
15
28
39
50
61
70
80
89
97
107
63
95
122
149
177
201
231
250
277
301
11
22
32
41
51
61
71
80
90
100
45
54
64
75
86
99
111
124
138
152
19
36
51
64
79
92
104
118
128
140
39
47
54
61
69
76
83
90
96
104
37
43
49
55
61
67
73
78
84
90
A Rajski’s Random Partitioning
BBayraktaroglu’s deterministic partitioning
CTouba’s binary search
D Touba’s linear partitioning
E Digging
FMulti-Stage Batching
G Doubling
H Hybrid: Batched-BS
I Hybrid: Batched Dig
Diagnosis time for scan chain of length 961
Experimental Results
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5000
0 100 200 300 400 500 600 700 800 900 1000
Batched DiggingBinary SearchDoubling
Multi-Stage Batching
Techniques that excel for small values of faults perform poorly for large values of faults and vice versa
Conclusions
We show that the BIST diagnosis problem corresponds to the established field of Combinatorial Group Testing (CGT)
We improve on existing techniques in CGT literature
We propose and adapt a number of algorithms from CGT to the BIST diagnosis problem
Future Work Competitive CGT techniques for theoretical benchmarking of various diagnosis techniques Non-adaptive diagnosis techniques using binary superimposed codes Diagnosis in the presence of unreliable tests, e.g., aliasing effects in compactors like Multiple-Input Shift Registers (MISR)
