A Hybrid Test Compression Technique for Efficient Testing of Systems-on-a-Chip

1. A Hybrid Test Compression Technique for Efficient Testing of Systems-on-a-Chip Aiman El-Maleh King Fahd University of Petroleum & Minerals, Dept. of Computer Eng., Saudi Arabia

2. Outline • Motivation • Test compression techniques • Geometric Shapes Compression Technique • FDR Compression Technique • EFDR Compression Technique • Hybrid Compression Technique • Experimental results • Conclusions

3. Motivation • With today’s technology, complete systems with millions of transistors are built on a single chip • Increasing complexity of systems-on-a-chip and its test data size increased cost of testing • Test data must be stored in tester memory and transferred from tester to chip • Cost of automatic test equipment increases with increase in speed, channel capacity, and memory. • Need for test data reduction is imperative • Test compaction • Test compression

4. Test compression techniques • Burrows-wheeler transformation & modified run-length coding [Yamaguchi et al., ITC 97] • Statistical coding based on modified Huffman codes [Jas et al., VTS 99] • Coding based on storing differing bits, decoding based on embedded processor [Jas et al., ICCD 99] • Variable-to-block run-length coding, encoding runs of 0’s followed by 1 [Jas et al., ITC 98] • Variable-to-variable run-length coding using Golomb codes [Chandra et al., VTS 2000] • Variable-to-variable run-length coding using FDR codes [Chandra et al., VTS 2001] • Primitive Geometric shapes based Compression [El-Maleh et al., VTS 2001] • Variable-to-variable run-length coding using EFDR codes [El-Maleh et al., ICECS 2002]

5. (x,y) (x,y) (x,y) d d (x,y) d d (x,y) Geometric Compression Technique: Used geometric shapes • Point: • Lines:

6. (x,y) (x,y) d d d d (x,y) (x,y) d1 (x,y) d2 Used geometric shapes- cont. • Triangles: • Rectangle:

7. Geometric compression technique: encoding algorithm • Test set sorting • Generate clusters of 0’s or 1’s efficiently encoded by geometric shapes • Test set partitioning • Test set partitioned into L segments • Each segment consists of K blocks • Each block is NxN bits • Block encoding • Do not encode block and store actual test data (00) • Encode block as filled with all 0’s (010) • Encode block as filled with all 1’s (011) • Encode 0’s by geometric shapes (10) • Encode 1’s by geometric shapes (11)

8. FDR Compression Technique • Based on run-length coding • A run is a consecutive sequence of equal symbols. • A sequence of symbols can be encoded using two elements for each run; • the repeating symbol and • the number of times it appears in the run • A variable-to-variable coding technique based on encoding runs of 0’sfollowed by a 1 • Designed based on the observation that frequency of runs decreases with the increase in their lengths. • Assign smaller code words to runs with small length and larger code words to those with larger length

9. FDR Codes • Prefix and tail of any codeword are of equal size • In any group Ai, the prefix is of size i bits. • When moving from group Aito group Ai+1, the length of the code words increases by two bits

10. Extended FDR (EFDR) Codes • FDR code extended by encoding both types of runs • An extra bit is added to beginning of a code word to indicate type of run

11. Proposed Hybrid Compression Technique • Combines Geometric compression technique with FDR or EFDR compression techniques • Main objective is to reduce the number of blocks encoded by storing the real test data

12. Experimental results • Benchmark circuits • Largest ISCAS 85 and full-scanned versions of ISCAS 89 circuits • Test sets • 14 different test sets • Dynamic compaction by Mintest [Hamzaoglu & Patel, ICCAD 98] • Static compaction by Mintest (Relaxed) • Compression ratio • (#Original Bits - #Compressed Bits)/#Original Bits

13. Comparison with Geometric & FDR Compression

14. Compression results of Geometric, FDR, EFDR, GFDR, and GEFDR

15. Analysis of block encoding for Geometric, GFDR, and GEFDR

16. Conclusions • Proposed hybrid compression scheme that combines Geometric compression with FDR (GFDR) or with EFDR (GEFDR) • Objective is to reduce the number of blocks encoded by real test data • GEFDR (GFDR) reduced blocks encoded by real data from 15% to 7% (10%) • In GEFDR, Blocks encoded by Geometric are 46% and those encoded by EFDR are 18%. • In GFDR, Blocks encoded by Geometric are 49% and those encoded by EFDR are 12%. • Hybrid compression schemes performed consistently better than Geometric • GEFDR achieved the best results and improved compression on average from 59% to 62%.