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 Aiman El-Maleh King Fahd University of Petroleum & Minerals, Dept. of Computer Eng., Saudi Arabia

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

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

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

5. 5 Geometric Compression Technique: Used geometric shapes n Point: n Lines: n Point: n Lines: (x,y) Type1Type2Type3Type4 (x,y) d(x,y)d (x,y) d (x,y) d

6. 6 Used geometric shapes- cont. n Triangles: n Rectangle: n Triangles: n Rectangle: Type1Type2Type3Type4 (x,y)d (x,y) d (x,y) d (x,y) d (x,y)d1d2

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

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

9. 9 FDR Codes n Prefix and tail of any codeword are of equal size n In any group A i, the prefix is of size i bits. n When moving from group A i to group A i+1, the length of the code words increases by two bits n Prefix and tail of any codeword are of equal size n In any group A i, the prefix is of size i bits. n When moving from group A i to group A i+1, the length of the code words increases by two bits Group Run Length Group Prefix Tail Code word A100000 1101 A2210001000 3011001 4101010 5111011 A36110000110000... 13111110111

10. 10 Extended FDR (EFDR) Codes n FDR code extended by encoding both types of runs n An extra bit is added to beginning of a code word to indicate type of run n FDR code extended by encoding both types of runs n An extra bit is added to beginning of a code word to indicate type of run Group Run Length Group Prefix Tail Code word for 0 Runs Code word for 1 Runs A1100 000 100 21 001 101 A231000 01000 11000 401 01001 11001 510 01010 11010 611 01011 11011 A37110000 0110000 1110000.... 14111 0110111 1110111

11. 11 Proposed Hybrid Compression Technique n Combines Geometric compression technique with FDR or EFDR compression techniques n Main objective is to reduce the number of blocks encoded by storing the real test data n Combines Geometric compression technique with FDR or EFDR compression techniques n Main objective is to reduce the number of blocks encoded by storing the real test data Header Code Encoded Block 000 With real test data 001 With FDR or EFDR codes 010 As filled with 0’s 011 As filled with 1’s 10 With geometric shapes covering 0’s 11 With geometric shapes covering 1’s

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

13. 13 Comparison with Geometric & FDR Compression

14. 14 Compression results of Geometric, FDR, EFDR, GFDR, and GEFDR Circuit Orig. Bits Geom.FDREFDRGFDRGEFDR c26701025251.8543.8253.1154.1454.56 s359322115625.783.9945.6326.2744.93 s3841711315246.537.6652.3548.3751.45 s53782075851.5546.8550.8153.1253.18 s35932 d 2820878.12319.3680.3178.1281.71 s38417 d 16473662.22643.2760.5763.0965.23 s9234d3927357.2243.6145.8958.3957.87

15. 15 Analysis of block encoding for Geometric, GFDR, and GEFDR GeometricGFDRGEFDR Circuit#Blk#Fill #Shape Encod. #Real #FDR Encod. #Real #Shape Encod. #EFDR Encod. #Real c2670180569925703321684016 s35932442761911751825413012919641 s3841718722521484136121434858105953427 s5378351732205819346391856330 s35932d44256384238402334502 s38417d2704106814471891290220126112945354 s9234d6201504106036771323756035 AVG % 28.9755.8715.1648.7812.2310.246.1617.57.37

16. 16 ConclusionsConclusions n Proposed hybrid compression scheme that combines Geometric compression with FDR (GFDR) or with EFDR (GEFDR) n 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%) 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 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%. In GFDR, Blocks encoded by Geometric are 49% and those encoded by EFDR are 12%. n Hybrid compression schemes performed consistently better than Geometric n GEFDR achieved the best results and improved compression on average from 59% to 62%. n Proposed hybrid compression scheme that combines Geometric compression with FDR (GFDR) or with EFDR (GEFDR) n 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%) 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 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%. In GFDR, Blocks encoded by Geometric are 49% and those encoded by EFDR are 12%. n Hybrid compression schemes performed consistently better than Geometric n GEFDR achieved the best results and improved compression on average from 59% to 62%.