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L25 : Crosstalk-Concerned Physical Design (2)

L25 : Crosstalk-Concerned Physical Design (2). 1999. 10 Jun Dong Cho Sungkyunkwan Univ. Dept. ECE E-Mail : Jdcho@skku.ac.kr Homepage : vada.skku.ac.kr. Min-Crosstalk Top Down Global Routing Algorithm(1). Crosstalk-Critical Region : The region disturbed by crosstalk between two wires

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L25 : Crosstalk-Concerned Physical Design (2)

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  1. L25 : Crosstalk-Concerned Physical Design (2) 1999. 10 Jun Dong Cho Sungkyunkwan Univ. Dept. ECE E-Mail : Jdcho@skku.ac.kr Homepage : vada.skku.ac.kr

  2. Min-Crosstalk Top Down Global Routing Algorithm(1) • Crosstalk-Critical Region : The region disturbed by crosstalk between two wires • Crosstalk generated between random signal net i and j is m = number of crosstalk-critical region crosstalk between two net performed by global routing

  3. Min-Crosstalk Top Down Global Routing Algorithm(2) • We decide the routing pattern by the position of net that meets design specification. First, whole chip is divided in 4 plane, performs routing by determined routing pattern. Then, performs dividing previous divided plane into 4 plane, and this process performs recursively. • Channel Density : the maximum number of wire that passes one channel. • : the number of net which connects terminals between and .

  4. Min-Crosstalk Top Down Global Routing Algorithm(3) • The nodes represents information about routing pattern and channel density of each net. • The nodes positioned vertical lines represent different routing pattern of the same net. • We define the information of node as follows. • d(degree) : the number of node that is not for random node . • The edge represent crosstalk between two nodes, and we consider the crosstalk is 0 when the distance of nets is greater than . • Graph contains Routing pattern, Channel density and Information on crosstalk

  5. Min-Crosstalk Top Down Global Routing Algorithm(4) • G = ( V, E ), V = nodes, E = edges; STEP 1 : sorts the crosstalk between node and in ascending order, construct set Z and X. STEP 2 : compute for each net. STEP 3 : choose nodes that has smaller in vertical lines and compute total crosstalk and channel density STEP 4 : Reconstruct graph STEP 5 : Iterate STEP 2 ~ STEP 4 until and are equal. STEP 6 : Choose final result that has minimum crosstalk and meets channel density performed STEP 3.

  6. Min-Crosstalk Top Down Global Routing Algorithm(5) • Experimental Result

  7. An Optimal Track Assignment considering Crosstalk and Power Dissipation • Crosstalk cost-function Where is signal sensitivity between net i,j is overlapped length between net i,j is width between net i,j

  8. Problem Formulation • For Mapping Order for set S T,

  9. Previous Approach • Track assignment problem is similar to Traveling Salesman Problem(TSP) in general graph algorithm • TSP problem is known as NP-Complete. • Brute-Force algorithm : • Single interval clique : • Continuous interval clique(k interval) : • Dynamic Programming (greedy approach): • In General Cases, Heuristic approach is used. • Proposed Algorithm • Single interval clique : Find optimal solution in • Continuous interval clique: Propose Heuristic algorithm in

  10. Special Case I : Containment Interval Clique • The shape of Interval Clique Set is Containment : We can find mapping order that has minimum crosstalk in

  11. Special Case II : Monotone Interval Clique • The shape of Interval Clique Set is Monotone : We can find interval mapping order that has minimum crosstalk in

  12. General Case II : Algorithm 3 • Theorem : All Interval Set S consists of Containment interval clique set and Monotone interval clique set, so we use below algorithm < Algorithm 3> Step 1 : Clique-Partition ( ) Step 2 : Apply Algorithm1( ) and Algorithm2( ) Step 3 : Merge_Clique ( )

  13. The case of Single interval clique • Procedure Merge_Clique process is only available as below three process.

  14. The case of Single interval clique : In general case • Conclusion : Using Algorithm 3, We can find interval mapping order that have minimum crosstalk for Single interval clique in general case. In this case computational complexity is

  15. Vertical Crosstalk • Crosstalk occurs not only horizontal wires but also occurs vertical wires that exist channel • Crosstalk by vertical wires has less size than horizontal wire • We can find the LONG-SHORT arrangement order by the method of horizontal wires

  16. Example of Single interval clique • : Sepcial case Track no. is 4 • Using 45O wire pattern, we can find interval mapping order that has minimum crosstalk for the case that track number is 4.

  17. Continuous interval clique • We can account track assignment problem in general cases of channel routing as track assignment problem of several numbers of divided sub-channel. • We can consider the solution of track assignment problem in general cases of channel routing as Minimization problem of number of LONG-LONG-LONG triple existed in total sub-channel.

  18. Continuous interval clique • Algorithm 4 [ time ] • Step 1 : run wirelength-based left-edge algorithm and Interval clique partitioning [ time] • Step 2 : interval type definition (LONG,SHORT)[ time] • Step 3 : find maximum LONG-SHORT ordered interval pair by using maximum-edge weight matching [ time] • Step 4 : make subchannel that have minimum LONG-LONG-LONG ordered interval triple by using minimum-edge weight matching [

  19. Experimental Result : Single interval clique

  20. Experimental Result : Continuous interval clique

  21. Experimental Result : Deutsch’s Difficult Routing Problem

  22. References and Suggested Readings • [1] Currie M, Sobolewski R, Hsiang TY. High-frequency crosstalk in superconducting microstrip waveguide interconnects. IEEE Transactions on Applied Superconductivity, V.9 N.2 P.3, 3602-3605, 1999 • [2] Chou M, White JK. EFFICIENT FORMULATION AND MODEL-ORDER REDUCTION FOR THE TRANSIENT SIMULATION OF THREE-DIMENSIONAL VLSI INTERCONNECT, IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems, V.16 N.12, 1454-1476, 1997 • [3] Vittal A, Mareksadowska M. CROSSTALK REDUCTION FOR VLSI. IEEE Transactions on Computer-Aided Design of Integrated Circuits & Systems, V.16 N.3, 290-29856, 1997. • [4] Yen-Tai Lai, Chi-Chou Kao, Wu-Chien Shieh. A Quadratic Programming Method for Interconnection Crosstalk Minimization. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems -, 270-273, 1999 • [5] Zemo Yang, Samiha Mourad. Deep Submicron On-chip Crosstalk. Proceedings of the 16th IEEE Instrumentation and Measurement Technology, 1788-1793, 1999 • [6] Lee, Mankoo. Fringing and coupling interconnect line capacitance model for VLSI on-chip. Proceedings of the IEEE International Symposium on Circuits and Systems, 1996 • [7] Hai Zhou and D.F.Wong. Crosstalk-Constrained maze Routing Basd on lagrangian Relaxation. Proceedings of the 1997 IEEE International Conference on Computer Desin : VLSI, 1997 • [8] Prashant Saxena, C. L. Liu. Crosstalk Minimization using Wire Perturbation. In Proc. Design Automation Conference, 1999 • [9] Hai Zhou, D. F. Wong. Global Routing with Crosstalk Contstraints , In Proc. Design Automation Conference, 1998 • [10] Hsiao-Ping Tseng, Louis Scheffer, Carl Sechen, Timing and Crosstalk Driven Area Routing,In Proc. Design Automation Conference, 1999 • [11] Tilmann Stohr, Markus Alt, Asmus Hetzel, Jurgen Koehl, Analysis, Reduction and Avoidance of Crosstalk on VLSI Chips, International Symposium on Physical Design, 1998

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