Power/Ground Network Aware and Row- Based Solutions to the Crosstalk Driven Routing Problem

Power/Ground Network Aware and Row- Based Solutions to the Crosstalk Driven

Routing Problem

Jinghong Liang,Tong Jing,

Xianlong Hong Jinjun Xiong, Lei He

CS&T Department EE Department

Tsinghua University UCLA

Beijing 100084, China Los Angeles, CA, USA

Speaker: Jinghong Liang

April 19, 2023 Asicon2005,Shanghai,China 2

Outline

1. Introduction

2. Our Work (Power/Ground Network

Aware and Row- Based Algorithm)

3. Experimental Results & Discussions

4. Conclusions


Backgrounds

Global routing plays an important role in very/ultra large scale integrated circuits (VLSI/ULSI) physical design

The progress in VLSI/ULSI enables system-on-a-chip (SOC) integration instead of system-on-a-board (SOB) integration

Chip design is with greatly shrinking of geometries and giga-hertz clock frequencies

All these advances enable us to get high-performance chips However, one of the great concerns is coupling effects and

crosstalk Crosstalk elimination has become a challenge to global routing

VLSI / ULSIVLSI / ULSI

System-On-a-Chip (SOC)System-On-a-Chip (SOC)

Clock frequency increasesClock frequency increases

Coupling effects and Coupling effects and crosstalkcrosstalk

New New challenge to global routing


Previous Work (1)

The existing works can be divided into three categories

Noise modeling Noise minimization Simultaneous noise minimization and performance optimization


Simultaneous noise minimization and performance optimization• [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ASICON, 2

003]----(PO-GR) • [J. Y. Xu, X. L. Hong, T. Jing, L. Zhang, J. Gu. ASP-DAC, 2004]• [ T. Jing, L. Zhang, J. H. Liang, J. Y. Xu, X. L. Hong, J. J. Xiong, L. He.

ASP-DAC, 2005, ]----(AT-PO-GR)

All proposed performance optimization global routing algorithms considering crosstalk reduction. The first mainly focuses on coupling capacitance and uses spacing method. The second considers coupling inductance and is based on shield insertion.The last obtain routing solutions with less routing area and greatly decrease running time.

• [L. Zhang, T. Jing, X. L. Hong, J. Y. Xu, J. J. Xiong, L.He. ISCAS, 2004]----(T-PO-GR)

Presented an efficient RLC crosstalk reduction algorithm

Previous Work (2)


Outline

1. Introduction




4. Conclusions


Global Routing Graph (GRG) with P/G network

GRC1

v1 v2 edge GRG

Chip P/G

network ...

...


Our Major Contribution

The major contribution of this paper is a power/ground network aware and row-based solution to the crosstalk driven routing problem.

The proposed algorithm can achieve more than 72% on average improvements for the adjacent edges while considering power/ground network, which greatly reduces potential vias.

Goal: to meet the practical applications and reduce potential vias


Problem Formulation

otherwise. 0,

, netby used is edge 1, itSit

n eN

i

N

ttit lSL

1 1

Then we have

Minimize

;,1

EtcosnSf ttt

N

iitt

n

);(,),,(),( isjNijiTjiT D

);(,, isjNiLSKLSK ijij

Subject to:

Let

(1)

(2)

(3)

• Formula(1) is the congestion constraint, which forbids the overflow on each GRG edge• Formula(2) guarantees the actual delay value from source i to sink j, T(i, j), is no more than the given timing constraint TD (i, j)• Formula(3) sets the upper bound of LSK, , for each source sink pair ij.ijLSK


LSK Model and Tabu Search

LSK Model for RLC Crosstalk EstimationOur crosstalk elimination is based on LSK model, which can be seen in [L. He and K. M. Lepak. ISPD, 2000]

Tabu Search

It is a famous algorithm and and be seen in many references.


Incongruous Grid Problem

Since we assume that shields provided by P/G network are as long as three GRG edges, the previous routing results should be improved to meet the practical applications.


Row-Based Solution

Net1

Net1

edge

GRG

The “dog-leg” problem.

Segments of the same net in adjacent GRG edges but are in different tracks (denoted by the order in the global routing phase), which makes more potential vias in detailed routing. Two segments of Net1 are not in the same track.


Our Methods(1)

1. Obtain Row-Based Solution(1) We still use Tabu search method to eliminate crosstalk noise.

The former cost formula of a GRG edge in AT-PO-GR is

cost(x) = w1 c1 + w2 c2 + w3 c3 + w4 c4

where w1, w2, w3, and w4 are the weights that equal to 13, 2, 13, and 10, respectively. c1 is the number of adjacency of sensitivity rate, c2 is the sum of violation Keff value, c3 is the number of Keff violation, and c4 is the number of shield inserted.


1. Obtain Row-Based Solution(2) But we use a new cost formula as follows to take the “dog-leg”

problem into consideration.

cost(x) = w1 c1 + w2 c2 + w3 c3 + w4 c4 + w5 c5

where c1,c2,c3,c4,w1,w2,w3 and w4 are the same as that of former cost formula, but we add w5 and c5 here. w5 equals 15, c5 = (1- a / b), a is the number of the adjacent segments of a net in the same tracks, b is the capacity of the GRG edge. So if a is bigger, the cost is smaller.


2. Tackle Incongruous Grid Problem(1) In former algorithm like AT-PO-GR, we assumed that

shields are as long as one GRG edges, which did not take actual P/G network into consideration.

Aware of P/G network, we assume that the horizontal shields are as long as 3 GRG edges. We try to make the 3 adjacent horizontal GRG edges have the same shield order by using the following method.

Our Methods(2)


2. Tackle Incongruous Grid Problem(2)Firstly, we partition all the horizontal GRG edges into edge groups, each of which includes 3 adjacent edges.

Then, in the same edge group, we can get the critical edge, which has the largest shield number. After that, we let the same shields track (i.e., the same shield order) in the other two edges (non-critical edges).

At last, we can adjust the segments in the non-critical edges to make use of the assigned shields.


Outline

1. Introduction




4. Conclusions


Experimental Environments

Circuits Number of nets GRG grids

C2 745 9*11

C5 1764 16*18

C7 2356 16*18

S13207 4953 24*26

AVQ 21581 65*67

Parameters Setting

LSK bound at each sink is set to be 1000

Na=350, Nb=20, Nc=10, and Tabu length=3

Benchmark Data

Platform

Hardware: sun V880 fire workstationSoftware: gcc2.9.1, solaris5.8


AT-PO-GR [t. Jing, L. Zhang, J. H. Liang] Proposed performance optimization global routing algorithms considering crosstalk reduction. It obtain routing solutions with less routing area and running time.

RB denotes the algorithm to get a row-based solution. IG denoted the algorithm considering incongruous grid problem.

We will compare our RB and IG with the above algorithms focusing on area, running time, etc.

In Comparison with Typical Algorithms


COMPARSION OF NUMBER OF ADJACENT EDGES HAVE SAME TRACK POSITION

Circuits AT-PO-GR RB IG

C2 116 339 202

C5 361 413 654

C7 382 416 797

S13207 1382 2322 4770

Avq 3207 5793 12513

Aver imp ------ 72.84% 159.85%


COMPARSION OF TOTAL WIRE LENGTH


C2 462204 465886 465886

C5 1320742 1327700 1327700

C7 1516366 1520446 1520446

S13207 9881044 9894684 9894684

Avq 9899034 9873887 9873887

Aver imp ------ 0.29% 0.29%


COMPARSION OF TOTAL RUNNING TIME


C2 87.21 70.44 98.08

C5 257.93 212.20 275.13

C7 331.25 279.21 345.41

S13207 2049.16 1436.15 1822.97

Avq 6171.94 5612.33 6479.56

Aver imp ------ 18.33% -3.47%


COMPARSION OF TOTAL AREA


C2 168*204 174*203 175*203

C5 304*332 301*333 302*333

C7 342*365 360*377 364*377

S13207 1208*1410 1203*1420 1216*1420

Avq 1216*1001 1215*1003 1223*1003

Aver imp ------ -2.30% -3.08%


Outline

1. Introduction




4. Conclusions


Conclusions

A performance and RLC crosstalk driven routing algorithm considering P/G network and row-based solution is presented in this paper.

The experimental results show this algorithm can

(1) take P/G network into consideration to meet the practical applications,

(2) and can give a row-based routing solution to minimize potential vias, which is useful for good manufacturability.


Future Work

As our future work, we plan to make our algorithm more practical to real chip routing, and design better strategies for crosstalk elimination.


Thank you!Thank you!Jinghong LiangJinghong Liang(( 梁敬弘梁敬弘 )) Dept . of CST, Tsinghua Univ.Beijing 100084, P. R. ChinaTel.: +86-10-62785428Fax: +86-10-62781489E-mail: [email protected].

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Documents

Power/Ground Network Aware and Row- Based Solutions to the Crosstalk Driven Routing Problem