2009Efficient test pattern compression techniques based on complementary Huffman coding

Efficient Test Pattern Compression Techniques Based on Complementary Huffman CodingShyue-Kung Lu, Hei-Ming Chuang, Guan-Ying Lai, Bi-Ting Lai, and Ya-Chen HuangDepartment of Electronic Engineering, Fu-Jen Catholic UniversityTaipei, Taiwan, 242, R.O.Csklu@.twAbstract⎯In this paper, complementary Huffman encodingtechniques are proposed for test data compression of complex SOC designs during manufacturing testing. The correlations of blocks of bits in a test data set are exploited such that moreblocks can share the same codeword. Therefore, beside the compatible blocks used in previous works, the complementary property betweens blocks can also be used. Based on thisproperty, two methods are proposed for Huffman encoding. According to this technique, more blocks will share the same codeword and the size of the Huffman tree can be reduced. This will not only reduce the area overhead of the decoding circuitry but also substantially increase the compression ratio. In order to facilitate the proposed complementary encoding techniques, a don’t-care assignment algorithm is also proposed. According to experimental results, the area overhead of the decompression circuit is lower than that of the full Huffman coding technique. Moreover, the compression ratio is higher that that of the selective and optimal selective Huffman coding techniques.I. I NTRODUCTIONDue to the ever-increasing complexity of SoC designs, a large amount of test patterns should be sent from the ATE’s to test embedded cores through the A TE channels. However, since the bandwidth of ATE channels and the capacity of ATE memory are limited, the cost of testing and test application time will increase considerably. To alleviate these problems, test compression techniques are usually adopted in today’s SOC era. There are three kinds of test compression techniques⎯linear-decompression-based scheme, broadcast-scan-based scheme [1], and code-based scheme [2-10].The code-based scheme is appropriate to compress the pre-computed test set without requiring any structural information of IP cores. In [3, 4], new dictionary-based compression schemes are proposed. Due to the regularity of the schemes, the advantages of a multiple-scan architecture can be preserved, and very low test time can be achieved. In [2], the RLE (run-length encoding) techniques used in JPEG still image compression systems are used to reduce test data and to make the area overhead almost negligible. Test compression techniques based on full Huffman encoding are proposed in [5, 6, 7, 8]. However, the size of the decoder will increase exponentially as the encoded symbols increase [5]. To cure this problem, the selective Huffman encoding technique was proposed in [6]. It only encodes the symbols with higher occurrence frequencies. The size of the decompression circuit can be reduced substantially. The technique was further improved in [7] by the optimal selective Huffman coding technique, which regards all non-encoded symbols as one symbol.In this paper, complementary Huffman encoding techniques are proposed. The correlations between blocks of bits in the test set are exploited to further reduce the size of Huffman tree. That is, more blockss that are compatible or complementary compatible can be merged and encoded with the same codeword. Two methods are proposed to encode compatible and complementary compatible blocks⎯Method 1 and Method 2. In order to maximum the merging process, a don’t-care assignment algorithm is also proposed. The size of the Huffman tree can be reduced significantly. Moreover, according to experimental results, the compression ratio will achieve 45% to 87% with Method 1, and achieve66% to 93% with Method 2 by using ISCAS89 benchmark circuits. The area overhead for implementing our decompression circuit is lower than that of the full Huffman technique.II. O VERVIEW O F T HE C OMPLEMENTARY H UFFMANC ODING T ECHNIQUESHuffman coding technique is basically a statistical coding scheme, which is a fix-to-variable coding scheme. It represents data blocks of fixed length by variable length codewords. Symbols occur more frequently have shorter codewords than symbols that occur less frequently. This will reduce the average number of bits for a codeword. Therefore, compression is achieved. An example of deriving the Huffman code is shown in Fig. 1 [6]. In this example, the test set is divided into 4-bit blocks. Table 1 [6] shows the frequency of occurrence of each of the possible blocks. The compression ratio is determined by how skewed the frequency of occurrence is.978-1-4244-2587-7/09/$25.00 ©2009 IEEE0010 0100 0010 0110 0000 0010 1011 0100 0010 0100 0110 0010 0010 0100 0010 0110 0000 0110 0010 0100 0110 0010 0010 0000 0010 0110 0010 0010 0010 0100 0100 0110 0010 0010 1000 0101 0001 0100 0010 0111 0010 0010 0111 0111 0100 0100 1000 0101 1100 0100 0100 0111 0010 0010 0111 1101 0010 0100 1111 0011Fig. 1: The example test set divided into 4-bit blocks.Table 1: Huffman Coding of the example [6]In this example, 13 symbols are used to construct the Huffman tree. The correlations between symbols are not exploited. We say that two symbols S i and S j are complementary compatible if the corresponding bits of these two symbols are bit-wise complementary and can be merged as a new symbol S i, j. For example, in Table 1, S1 (0100) and S7 (1011) are complementary compatible. Therefore, they can be merged as a new symbol S1,7. Similarly, S0 (0010) and S10 (1101) are complementary compatible and can be merged as S0, 10. The merged results of the symbols in Table 1 are shown in Table 2. The “Joint Frequency” column denotes the accumulated probability of symbols S i and S j. From this table we can see that instead of the original 16 symbols, we only need to encode the 8 merged symbols. Therefore, the size of the Huffman tree can be reduced significantly. Moreover, the skewing of the occurrence probabilities is helpful for the compression of test data. The average length of codewords can also be reduced significantly. This will in turn increase the compression ratio.III. D ON’T C ARE A SSIGNMENT T ECHNIQUESIn general, test patterns generated by commercial ATPG tools contain massive unspecified bits (don’t-care bits) that can be assigned with 1’s and 0’s in a way to skew the frequency distribution. This is helpful to maximize the compression efficiency. In [6], two don’t care assignment techniques are proposed. However, only compatible characteristics are used in their techniques. Two blocks areTable 2: Merged Symbols of Table 1 compatible if there is no conflict in any bit position of the two blocks. For our complementary coding techniques, beside the compatible blocks are exploited, complementary blocks are also searched. Therefore, the Alg_comp algorithm is proposed in this paper to perform don’t care assignment.In Alg_comp., we first search for the most frequently occurring unspecified block F1. Thereafter, it is compared with the next most frequently occurring unspecified block F2. If there is no conflict in any bit position, these two blocks are merged by specifying every bits position if there is specified bit in either block. All F2 blocks in test set are appended with 0 to indicate that it is merged with F1 block. For example, if block F1 00XX is merged with block F2 0X1X, the result is 001X. All F2 blocks in the test set will be changed to 0001X.Alternatively, if there is a conflict, F1 is compared with the complement of F2. If there is no conflict in any bit position, then they are merged. All F2 blocks in the test set are appended with 1 to indicate that it is merged with F1 block in its complementary form. For example, if F1 is 00XX and F2 is 1X0X, block 00XX is merged with block 0X1X, which is the complement of block 1X0X. The resulted block is 001X and all F2 blocks in the test set are changed to 1001X. Thereafter, F1 is compared with all the other unspecified blocks in decreasing order of frequency and merged if possible. This process is finished if there is no more block that can be merged with F1. This process is then repeated until there is no more blocks that can be merged in the test set. Any remaining X’s can be randomly assigned 0’s or 1’s since it has no effect on the compression ratio.Consider the example test set shown in Fig. 2(a), the test set contains five unique unspecified blocks⎯1X01, 10X1, 01XX, 01X1, and 101X. Let B uniq denote the set of unique blocks. In the test set, the frequency of occurrence of block 10X1 is 3, that of blocks 1X01 and 01XX is 2, and that of other blocks is 1. After applying the first step of Alg_comp., the most frequently occurring unspecified block 10X1 is found. It is compared with 1X01, which is the next most frequently occurring unspecified block. SinceSymbol Freq. Block Huff. Code S022 0010 10S113 0100 00S27 0110 110S3 5 0111 010S4 3 0000 0110 S5 2 1000 0111 S6 2 0101 11100 S7 1 1011 111010 S8 1 1100 111011 S9 1 001 111100 S10 1 1101 111101 S11 1 1111 111110 S12 1 0011 111111 S130 1110 -S140 1010 -S150 1001 - Symbol Joint Freq. Pattern S0, 1023 0010 S1, 714 0100 S2,157 0110 S3, 57 0111 S4, 11 4 0000 S6, 14 2 0101 S8, 12 2 1100 S9, 13 1 0001there are no conflicts, these two blocks can be merged and the result is 1001. All 1X01 in the test set are appended with 0. The merged block 1001 is compared with other unspecified blocks. It is merged with 10XX, which is the complement of the unspecified block 01XX. All 01XX blocks in the test set are appended with 1. At this time, B uniq = {1001, 01X1, 101X} and blocks 10X1, 1X01, and 01XX are transferred to 01001, 01001, and 11001, respectively.This process is repeated and 01X1 is merged with 010X, which is the complement of the unspecified block 101X. Since there are no more unspecified blocks that can be merged in the test set, therefore, the process is finished. The blocks 01X1 and 101X are changed to 00101 and 10101, respectively. Finally, the set B uniq is {1001, 0101}. The final test set is shown in Fig. 2(b).1X01 10X1 1X01 01001 01001 0100110X1 01XX 01X1 01001 11001 0010110X1 101X 01XX 01001 10101 11001(a) (b)Fig. 2: (a) Test set before don’t care assignment, and (b)after applying Alg_comp.IV. C OMPLEMENTARY H UFFMAN E NCODING T ECHNIQUES When all don’t-care bits of unspecified blocks are assigned by Alg_comp algorithm, the first bit of each merged block denotes whether the block is complementary merged or not. In this section, two methods⎯Method 1 and Method 2 are proposed for encoding the specified blocks. Test volume and area overhead of the decoding circuitry can be reduced significantly by using these two methods. Method 1: One Control Bit AddedAfter using the alg_comp algorithm for filling the don’t care bits, the blocks with complementary relationship are regard as one symbol to reduce the number of symbols such that it can reduce the size of Huffman tree. However, in order to distinguish the complementary pair, one control bit C is appended to the codeword of the complementary pair. This control bit is used to indicate the decoder whether the decoded blocks should be complemented or not.An example is shown in Fig. 3 and Table 3. The blocks 0110 and 1001 are a complementary pair. Therefore, they share the same symbol S0. Similarly, blocks 1010 and 0101 share the symbol S1. The occurrence frequencies of all symbols are shown in the third column. All symbols are encoded based on the conventional Huffman coding techniques. However, one control bit is appended to each codeword. For example, the original Huffman code is 0 for blocks 0110 and 1001. However, a “0” is appended to form the final codeword for block 0110 and an “1” is appended to form the final codeword for block 1001. In the decoding circuitry, this control bit is used to determine whether the decoded blocks should be complemented or not.00110 00110 10110 00110 00110 00110 10110 10110 00110 00110 00110 00110 00110 00110 10110 00110 00110 00110 00110 00110 00110 00110 01010 01010 00110 00110 00110 00110 00110 00110 10110 00110 00110 00110 00110 00110 01110 00110 00110 00111 11010 00111 10110 00110 00110 00110 00011 10110 10111 00110 11010 00110 00110 00110 00110 11010 01010 10110 00110 10110 Fig. 3: The test set after don’t-care assignment (block size= 4)Table 3: Complementary EncodingSymbol Freq. BlockMethod 1 Method 2HuffmanCodeFinalCodeHuffmanCodeFinalCode S0 49400110009100110 100S group 13------------------10 ------S1 6310101001011011030101110 10110 S2 320011110011011101110111001110 101110 S3 111111111001110111101111000000------------S4 110111111101111111111111101000------------Method 2: Regarding all complementary blocks as a symbolFor Method 1 encoding technique, one control bit is required for each codeword. This will impact the compression ratio. Therefore, in order to substantially improve the compression ratio and reduce the area overhead for Huffman decoding. Method 2 treats all complementary blocks as a symbol (S group). For example, in Table 3, the complementary blocks 1001, 0101, and 1100 are treated as symbol S group. The occurrence frequency of S group is 13. This symbol is then encoded along with other symbols by using the conventional Huffman coding technique. The Huffman code for S group is 10 as shown in this table. This control code is then appended to the Huffman code of other symbols to form the final code of complementary blocks. For example, The Huffman code for block 0110 is 0. When the control code “10” is appended, the final code for block 1001 is 100.V. EXPERIMENTAL RESULTS Experimental results based on ISCAS89 benchmark circuits are shown in Table 4. The block size can be 4, 8, 12, or 16 bits. The results of selective Huffman coding, optimal selective Huffman coding, and the methods proposed in this paper are compared as shown in this table. We can see thatTable 4: Comparisons of compression ratiothe compression ratio of Method 2 is better than that of Method 1. Moreover, the proposed two methods usually have higher compression ratio than the selective and optimal selective Huffman coding techniques.The results of hardware overhead of the decoder are shown in Table 5. Since Method 1 and Method 2 consider the complementary relationship between blocks, the number of leaf nodes is reduced. Therefore, the number of states will be reduced in the decoder. In this table, we can see that the area overhead of Method 1 and Method 2 is smaller than the full Huffman encoding technique. If the block size increases, the compression efficiency is better. However, the hardware overhead will increase. Therefore, the block size provides an easy way to tradeoff between area overhead and compression efficiency. Although the area overhead of the proposed complementary Huffman coding technique is larger than that of the selective Huffman coding technique, it has 10％~30% improvement in compression ratio.Table 5: Comparisons of area overhead.VI. C ONCLUSIONSIn this paper, complementary Huffman coding techniques are proposed for test compression of SOC designs. Instead of exploiting compatible blocks as the conventional techniques, complementary compatible blocks are also searched to further increase the compression ratio. Two methods are proposed for the encoding of blocks. For don’t-care assignment, the Alg_comp algorithm is proposed. According to experimental results, the area overhead of the decoding circuitry is lower than that of the full Huffman coding technique. Moreover, the compression ratio is higher that that of the selective and optimal selective Huffman coding techniques. Although the area overhead is larger than [6], however, the compression ratio is much better than it.R EFERENCE[1] K. J. Lee, J. J. Chen, C. H. Huang, ”Broadcasting test patternsto multiple circuits,” IEEE Trans. Computer-Aided Des. Integr.Circuits and Syst., vol. 18, no. 12, pp. 1793-1802, Dec. 1999. [2] H. Ichihara, Y. Setohara, Y. Nakashima, and T. Inoue, “Testcompression/decompression based on JPEG VLC algorithm,”in Proc. Asian Test Symposium., Oct. 2007,pp. 87-90.[3] A. Wurtenberger, C. S. Tautermann, and S. Hellebrand, Datacompression for multiple scan chains using dictionaries withcorrections,” in Proc. Int’l Test Conf. (ITC 2004), pp. 926-935, Oct. 2004.[4] F. G. 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IEEESymp.Circuits and System. vol. 2, pp. 681-684, May 2004.CircuitSelective Huffman Optimal Selective Huffman Method 1 Method 28 enc. dist. blocks 16 enc. dist. blocks 8 enc. dist. blocks 16 enc. dist. blocks--- ---4 8 12 16 8 12 16 4 8 12 16 8 12 16 4 8 12 16 4 8 12 16S5378 28.9 50.1 53.0 53.0 50.2 55.1 53.8 47.1 54.754.951.155.857.5 55.046.6967.6766.4057.81 66.15 75.54 70.8760.46 S9234 30.0 50.4 50.7 46.1 50.2 54.2 51.0 51.4 55.351.846.157.756.8 51.949.2773.4880.0782.11 70.41 82.65 85.4485.36 S13207 45.6 69.2 76.6 78.6 69.2 77.1 79.7 69.9 80.283.483.180.684.3 84.549.9374.8483.1587.12 74.53 86.92 91.1293.12 S15850 38.8 60.0 63.6 61.6 59.9 65.6 64.8 62.1 67.967.363.669.370.4 67.249.8874.4082.3485.79 73.49 85.00 88.9990.36 S38417 34.9 55.3 56.9 54.4 55.5 58.9 57.3 55.9 60.959.355.262.861.8 58.650.0074.8478.9780.08 74.65 86.99 87.3186.29 S38584 37.8 58.5 62.2 61.7 58.5 63.9 64.1 60.4 65.465.263.366.968.0 66.149.9474.8982.7186.15 72.31 84.82 88.7390.3Circuit Full Huff. SelectiveHuff. Method 1Method 2S5378 79.2 10.4 38.57 41.83S9234 51.1 8.6 16.8 17.78S13207 23.6 3.7 6.96 7.14S15850 26.1 4.5 8.22 8.90S38417 21.3 1.3 1.3 1.52S38584 19.7 1.3 1.75 1.88。