A Novel Crosstalk Estimator after Placement

Abstract

In this paper, we propose a probabilistic method to estimate intra-grid wirelength of nets after placement or global routing.
Results of incorporating this method in the previous probabilistic coupling capacitance and crosstalk estimation scheme show
its efficiency in detecting noisy nets before having detailed information of wire adjacency. Our general method improved the
number of correctly detected noisy nets by 15% on average. In a second improvement, the directed version of this method increased
the number of correct detections by 19% and decreased the number of false detections.

Full text

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A Novel Crosstalk Estimator after Placement1
Arash Mehdizadeh1, Morteza Saheb Zamani2

1,2 Compute Engineering Department, Amirkabir University of Technology,
Tehran, Iran.
{a_mehdizadeh, szamani}@aut.ac.ir
Abstract. In this paper, we propose a probabilistic method to estimate intra-
grid wirelength of nets after placement or global routing. Results of
incorporating this method in the previous probabilistic coupling capacitance
and crosstalk estimation scheme show its efficiency in detecting noisy nets
before having detailed information of wire adjacency. Our general method
improved the number of correctly detected noisy nets by 15% on average. In a
second improvement, the directed version of this method increased the number
of correct detections by 19% and decreased the number of false detections.
Keywords: Physical Design, Placement, Routing, Coupling Capacitance,
Crosstalk Noise.
1 Introduction
Nowadays, crosstalk noise introduced by coupling capacitance became one of the
most important issues of design closure. Due to the giga-scale number of elements in
the recent designs, crosstalk mitigation should be considered in the earlier physical
design stages, especially placement. There have been a number of studies on wiring
congestion reduction during placement [4], [5], [6], yet just a few deal with crosstalk
explicitly [1]. In addition to the coupling capacitance, other parameters such as driver
strength and coupling location affect the crosstalk noise significantly [3]. The 2-pi
model from [3] is an elegant analytical model which takes into consideration many of
the first-order parameters such as coupling capacitance and driver and wire resistance.
To use this model, these parameters must be available which some directly depend on
the precision of routing estimation.
To enhance the crosstalk estimation schemes during or after placement, where
there is not enough routing information, we introduce a probabilistic method to
estimate the detailed routing results inside global routing grids. Using our method, we
can derive approximate length of wire-segments of each net inside every global
routing grid. Feeding this information to an efficient wire adjacency and crosstalk
estimation method like [2], we can extract the first order parameters of the 2-pi
crosstalk model. Hence, it is possible to derive the crosstalk map and use it as
guidance for crosstalk reduction.

1 This work is supported by Iran Telecommunications Research Center (ITRC)

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2 Intra-Grid Routing Estimation without Internal Connection
Consider that we have the global routing estimation or information of the nets
traversing global grids. For a horizontal traversing net (Fig.1. a), the two intersections
on the vertical left and right edges can be placed in different vertical distances. We
call this a horizontal 2-pass net. If the width and length of the grid are W and L
respectively, this vertical distance can vary from 0 to L. We call this conditional
vertical distance (CVD). This net should also traverse the horizontal distance from
one edge to the other one. This horizontal distance is equal to W and we call it the
forced horizontal displacement (FHD).
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Fig. 1. Wirelength computation for (a) horizontal 2-pass net, (b) vertical 2-pass net, (c) 3-pass
net, (d) 4-pass net.
Another case in which a net traverses the grid vertically is shown in Fig.1. b. We call
this a vertical 2-pass net. If the boundary pins can be placed on any of the tracks of
the edges with equal chance, it can be proved that the average values of coefficients K
and K' will be equal to 0.5. These values are a little pessimistic which can lead to false
detections. As a result, one can examine the length of horizontal and vertical segments
in these cases for a set of different designs with a specific detailed router and extract
average values for the K and K' coefficients. We did this practice for a set of 6 test
circuits using the router proposed in [7]. The results are presented in section 4.
Having the average wirelength of horizontal and vertical segments of the 2-pass nets,
we can analyze more sophisticated cases in which the traversing nets pass more than
two edges of the grid (Fig.1. c, d). In these cases vertical/horizontal paces (VP/HP)
will be added to the conditional vertical/horizontal displacements respectively.
3 Intra-Grid Routing Estimation with Internal Connection
There are also cases in which there is one or more than one point in a grid that belong
to one net. In Fig. 2 (x0,y0), (xn,yn), (x1,y1), etc. show the coordinates of different points

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in the grid area. In Fig. 2, there are four internal points all belonging to the same net
which has also to be connected to the external connections going through the left,
right and up edges. Connection of internal points is estimated with a half-perimeter
routing (here, with two segments named A and B).
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(3)
Fig. 2. Computing wirelength with three external and four internal connections.
Equations 1-3 calculate the cost of connecting the half-perimeter to the edges. We
used X and Y indices to correspond a value to a wire-segment in the horizontal or
vertical direction respectively. In these equations the wire-segment nearest to a
specific edge is chosen for connection of the whole connected component to that
edge. For example the Equation denoted by Left(A), computes average wirelength of
connecting the half-perimeter connection to the left edge (which is through segment
A). Similar analysis can be conducted for the other patterns of traversal while having
internal connections. Due to the similarity, we did not repeat them here.
2 Experimental Results and Conclusion
To appraise our noise estimation methodology, we used routing feedbacks of a multi-
level routing framework introduced in [7]. Six test circuits of [7] were global and
detailed routed by the specified router. Table 1 presents the characteristics of these six
circuits along with the accuracy results of the following three different crosstalk
estimation schemes all using the method used in [2] for basic probabilistic coupling
capacitance estimation: A) Without using our proposed wirelength estimation method.
B) Using our methodology and setting K and K' coefficients to the general value 0.5
(general method). C) Using our methodology while measuring average values of K

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and K' based on the results of the detailed router (directed version). The # of Nets
column contains the number of two-pin nets in each of the six circuits after a
decomposition stage. After routing, information over the complete layout is given to
the extraction tool to determine the real # of Noisy Nets.
Table 1. Test circuits' specifications with results of different crosstalk estimation schemes.
False Detections Correct Detections
C
17
14
37
35
140
B
32
20
55
63
230
A
22
17
43
54
150
C
50
38
112
132
285
B
47
38
107
124
273
A
39
30
91
107
225
# of
Noisy
Nets
53
45
122
140
300
# of
Nets
Size (um) Circuit
3124
2774
6995
8321
21035
4330*2370
4020*2230
6590*3640
7040*3880
11430*6180
S5378
S9234
S13207
S15850
S38417
Correct Detections column represents the number of correctly detected noisy nets in
the aforementioned three cases. In order to obtain proper values for K and K', we
examined horizontal/vertical conditional displacement of all 2-passing nets in all the
test cases after detailed routing, using global routing bins of size 30pitch*30pitch. The
distribution of these two coefficients depends on such factors as grid size and
congestion. Nevertheless, the derived averages (K=0.2, K'=0.17) improved the general
method's Correct Detections while decreased False Detections (the number of falsely
detected noisy nets). As it is shown, the proposed approach (columns B and C)
increases correct detections by 15% on average. On the other hand, the general
method (column B) has more false detections due to its pessimistic estimations of the
wirelength. However, this pessimism is ameliorated in the directed method (column
C) by using more realistic coefficients.
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