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DPIMM-II 2003 UCSD VLSI CAD LAB Compression Schemes for "Dummy Fill" VLSI Layout Data Robert Ellis, Andrew B. Kahng and Yuhong Zheng ( Texas A&M University and UCSD) http://vlsicad.ucsd.edu Supported by MARCO GSRC

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DPIMM-II 2003 UCSD VLSI CAD LAB Outline Dummy Fill and Fill Compression Problem Our Contributions JBIG* Standards Loss/Lossless Compression Algorithms Experimental Results Conclusion and Future Research

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DPIMM-II 2003 UCSD VLSI CAD LAB Uneven features cause polishing pad to deform in Chemical- Mechanical Polishing (CMP) Post-CMP ILD thicknessFeatures CMP and Dummy Fill Interlevel-dielectric (ILD) thickness feature density Insert non-functional dummy features to decrease variation Dummy featuresPost-CMP ILD thickness Dummy feature explodes layout data volume, creates a bottleneck in the design-to-manufacturing handoff Dummy fill data compression is required

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DPIMM-II 2003 UCSD VLSI CAD LAB Fill Compression Problem 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 Compressed Layout Data 1: With features0: Without features A fill pattern can be expressed as a binary (0-1) matrix Problem: Given a 0-1 matrix B [m n] digitized from a dummy fill layout, compress it with the objective of minimizing output data size h Compression ratio r = m n/h One-sided loss Limited loss can improve compressibility Asymmetric loss: 1 0 okay! (fill geometry disappears); 0 1 not allowed (fill geometry appears)

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DPIMM-II 2003 UCSD VLSI CAD LAB General Flow for Compression Heuristics Segment data matrix into blocks Loss allowed? Applied one-sided loss to original data matrix Perform lossless compression on data matrix END Yes No

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DPIMM-II 2003 UCSD VLSI CAD LAB Our Contribution New compression heuristic algorithms on JBIG methods JBIG1 JBIG2-Pattern Matching and Substitution (PM&S) JBIG2-Soft Pattern Matching (SPM) Two loss mechanisms Proportional loss: relative fraction of 1’s allowed to be changed to 0’s Fixed “speckle” loss: absolute number of 1’s allowed to be changed to 0’s Asymmetric cover method that comprehends one-sided loss and improves the compression ratio

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DPIMM-II 2003 UCSD VLSI CAD LAB General Flow for Compression Heuristics Segment data matrix into blocks Loss allowed? Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix END Yes No Applied one-sided loss to original data matrix

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DPIMM-II 2003 UCSD VLSI CAD LAB JBIG* Standard JBIG (Joint Bi-level Image Experts Group) is an experts group of ISO, IEC and CCITT (JTC1/SC2/WG9 and SGVIII). Its goal is to define a compression standard for bi- level image coding JBIG1: international standard for lossless compression of bi-level images (ITU-T T.82) (1993) JBIG2: the first International standard that provides for both lossless and lossy compression of bi-level images (1999) JBIG* methods are based on Arithmetic Coding and Context-based Statistical Modeling

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DPIMM-II 2003 UCSD VLSI CAD LAB JBIG2 PM&S PM&S: Pattern Matching and Substitution Dictionary: reference blocks that used to match data blocks Extract and encode repeatable patterns

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DPIMM-II 2003 UCSD VLSI CAD LAB JBIG2 SPM SPM: Soft Pattern Matching Dictionary: reference blocks that used to match and coding data blocks Estimate bits probabilities based on data block and matched reference block, codes data in arithmetic coding

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DPIMM-II 2003 UCSD VLSI CAD LAB Dictionary Construction To achieve better compression ratio: Dictionary should contain as few reference blocks as possible to match a much larger number of data blocks Reference indices (pointing from data blocks to reference blocks) as shorter as possible Removing singletons from the dictionary will reduce the size of dictionary Asymmetric cover approach is applied to construct a dictionary for loss compression

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DPIMM-II 2003 UCSD VLSI CAD LAB General Flow for Compression Heuristics Segment data matrix into blocks Loss allowed? Asymmetric cover heuristic for one-sided loss Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix END Yes No

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DPIMM-II 2003 UCSD VLSI CAD LAB Asymmetric Cover Heuristic The problem of building a cover for a set of data blocks is an instance of the Set Cover Problem (SCP) Asymmetric cover: allows number of 1’s can be changed to 0’s, yet 0’s can not be changed to 1’s Our heuristic for constructing cover: views the data blocks as vertices of a graph with edge weights defined as: w(D 1, D 2 ) = min(t(D 1 ) – HD(D 1, D 1 ^ D 2 ), t(D 2 )-HD(D 2, (D 1 ^ D 2 )) D: data block, ^: bit-wise AND t(D) = the total allowable loss for D D 1 and D 2 covered by the same cover iff w(D 1, D 2 ) 0 Cover D = D 1 ^ D 2. Clustering data blocks 111111 and 111101

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DPIMM-II 2003 UCSD VLSI CAD LAB Description of Algorithm Pieces IndexDescriptionA1A2.1A2.2A2.3A3 Benchmark Compress matrix using JBIG1 Loss introduction Proportional loss Fixed speckle loss JBIG* lossless components JBIG2 PM&S JBIG2 SPM (lossless) Singleton exclusion & singleton data blocks compression by JBIG1 Compress dictionary JBIG1 on reference blocks compression

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DPIMM-II 2003 UCSD VLSI CAD LAB General Compression Algorithm Segment data matrix into blocks Asymmetric cover heuristic for one-sided loss Perform lossless compression (JBIG1, JBIG2 PM&S, and JBIG2 SPM) on data matrix END Yes No (A2.2) (A2.3) (A3) Exclude Singleton (A2, A3) JBIG2 PM&S (A2, A3) Dictionary Compression using JBIG1 (A2, A3) JBIG2 SPM (A2) Loss allowed?

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DPIMM-II 2003 UCSD VLSI CAD LAB Experimental Results A2.1 is the best lossless fill compression methods, with an average of 29.93% improvement to the Bzip2 A1 gives competitive compresstion ratios, with an average of 28.7% improvement to the Bzip2 A2.2 and A3 performs similar in all test cases Large loss yields better compression ratios.

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DPIMM-II 2003 UCSD VLSI CAD LAB Dictionary Fits SREFs 111000101 111000111 000101000 101000000 111000000 101000000 101000101 000101000 101000000 loss Dictionary entrySREF F F’ M M’

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DPIMM-II 2003 UCSD VLSI CAD LAB Geometry Compression Operators TYPE 1 TYPE 2 TYPE 3 equivalent to “GDSII AREF” TYPE 4 TYPE 5 TYPE 6 TYPE 7 TYPE 8 equivalent to “GDSII SREF” OASIS Repetition Types Original layoutFilled layout with area features in 9 repetitions

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DPIMM-II 2003 UCSD VLSI CAD LAB Conclusion and Future Research We have implemented algorithms based on JBIG* methods in combination with the new concept of one-sided loss to compress binary data files of dummy fill features. JBIG1 is quite effective. Our new heuristics A2-A3 and the fixed speckle loss heuristic offer better compression with slower runtime, especially as data files become larger Ongoing research examines synergies between fill generation and compression, as well as compression techniques that exploit constructs in the GDSII standard (AREF and SREF) and the new OASIS format (8 repetitions) for layout data.

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DPIMM-II 2003 UCSD VLSI CAD LAB Thank You!

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DPIMM-II 2003 UCSD VLSI CAD LAB

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DPIMM-II 2003 UCSD VLSI CAD LAB Experimental Results (Cont’d) For lossless compression, A1 is the most cost-effective method, taking only 2.7 longer than Bzip2 on average. A2.1 is nearly as cost effective, but takes 5.9 longer than Bzip2 on average. A3 is the most cost-effective proportional loss method, taking 3.7 longer than Bzip2 on average. The running time of A2.2 is 9.4 longer than Bzip2 on average with proportional loss ratio k=0.2 and 10.3 longer with k=0.4.

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