Niloy Ganguly Biplab K Sikdar P Pal Chaudhuri Presented by Niloy Ganguly Indian Institute of Social Welfare and Business Management. Calcutta 700 073 Email

Niloy Ganguly Biplab K Sikdar P Pal Chaudhuri

Presented byPresented by

Niloy GangulyNiloy Ganguly

Indian Institute of Social Welfare and Business Indian Institute of Social Welfare and Business Management. Calcutta 700 073Management. Calcutta 700 073

Email : [email protected] : [email protected]

Design of An On-Chip Test Design of An On-Chip Test Pattern Generator Without Pattern Generator Without

Prohibited Pattern Set (PPS)Prohibited Pattern Set (PPS)

ASP-DAC/VLSI Design 2002 2

• Introduction and OverviewIntroduction and Overview• Cellular Automata PreliminariesCellular Automata Preliminaries• Proposed Design of TPG Proposed Design of TPG • Experimental Results Experimental Results • Concluding RemarksConcluding Remarks

The Coverage

ASP-DAC/VLSI Design 2002

Problem Definitions

• Prohibited Pattern Set (PPS) – A set of Prohibited Pattern Set (PPS) – A set of patterns input of which sents the system patterns input of which sents the system into an unstable state.into an unstable state.

• Example : Toggle State of a flip flopExample : Toggle State of a flip flop• Design a TPG with the following featuresDesign a TPG with the following features

– It avoids the generation of such PPS It avoids the generation of such PPS – It maintains the randomness and fault It maintains the randomness and fault

coverage of a Pseudo Random Pattern coverage of a Pseudo Random Pattern Generator Generator

– Side by side it doesn’t add to any Side by side it doesn’t add to any hardware costhardware cost


Problem Definitions

• Non Max Length GF(2) Cellular Automata Non Max Length GF(2) Cellular Automata is employed to obtain the design criteriais employed to obtain the design criteria

• Design the CA in such a way so that it Design the CA in such a way so that it has large cycles free from PPShas large cycles free from PPS

• Design a TPG with the following featuresDesign a TPG with the following features– It avoids the generation of such PPS It avoids the generation of such PPS – It maintains the randomness and fault It maintains the randomness and fault

coverage of a Pseudo Random Pattern coverage of a Pseudo Random Pattern Generator Generator

– Side by side it doesn’t add to any Side by side it doesn’t add to any hardware costhardware cost


Clock

Combinational logic

CL

DFlip - Flop Q

From

left neighborFrom right neighbor

Cellular Automata MachineA powerful computing and modeling toolA powerful computing and modeling tool• 50’s - J von Nuemann50’s - J von Nuemann80’s - Wolfram80’s - Wolfram• A CA consists of an array of cellsA CA consists of an array of cells• A CA cell is essentially a memory element A CA cell is essentially a memory element

(D Flip flop) with some combinational (D Flip flop) with some combinational logic - an XOR and/or XNOR Gate logic - an XOR and/or XNOR Gate (additive) (additive)


Clock

Combinational logic

CL

DFlip - Flop Q

From

left neighborFrom right neighbor

Cellular Automata MachineA powerful computing and modeling toolA powerful computing and modeling tool• The cell is updated at every clock cycle The cell is updated at every clock cycle • The state of the cell is dictated by the The state of the cell is dictated by the

immediate neighborsimmediate neighbors• Typically termed as Two State Three Typically termed as Two State Three

neighborhood Cellular Automataneighborhood Cellular Automata


• The operation of XOR and XNOR rules can be The operation of XOR and XNOR rules can be conceived as mod two multiplication and conceived as mod two multiplication and additionaddition

• The operations thus can be mapped to The operations thus can be mapped to operations of Galois Field(2) giving rise to operations of Galois Field(2) giving rise to GF(2) GF(2) Cellular AutomataCellular Automata..

• The CA is characterized by a T matrix which is The CA is characterized by a T matrix which is essentially the dependency matrixessentially the dependency matrix

GF(2) Cellular Automata

1 0 0 0 01 0 0 0 00 1 1 0 00 1 1 0 0

T T = = 0 1 1 1 0 0 1 1 1 0 F =F = [1 0 1 0 1][1 0 1 0 1]0 0 0 1 1 0 0 0 1 1

0 0 0 0 10 0 0 0 1


• For 3-neighborhood CA, we have a band For 3-neighborhood CA, we have a band matrix matrix

• An XNOR CA is characterized by a An XNOR CA is characterized by a inversion vector F indicating the cells inversion vector F indicating the cells where XNOR operation has been where XNOR operation has been performed performed

GF(2) Cellular Automata

1 0 0 0 01 0 0 0 00 1 1 0 00 1 1 0 0

T T = = 0 1 1 1 0 0 1 1 1 0 F =F = [1 0 1 0 1][1 0 1 0 1]0 0 0 1 1 0 0 0 1 1

0 0 0 0 10 0 0 0 1


State Transition Behavior

• Group CA - All states lie on some CycleGroup CA - All states lie on some Cycle

0

9 15

613

7 12

3 14

11

5

2 8

1 4

10Non Maximum Length CA

1

21163 135

12 15 14 4 810 7

9

0

Maximum Length CA

Our TPG Design is based on this type of CA


2943

1112110

0151413

5678

Equal Length CA

State Transition Behavior

• Additive variant of Group CAAdditive variant of Group CA

Non Group CA : Cyclic/ Non cyclic and Non Reachable States

5

15

10

0

4

14

11

1

2

7

13

8

3

6

12

9

Our TPG Design is based on this type of CA


Overview of Design

Given PPSGiven PPS00001100000110

00000100000010

00010010001001

00001110000111

PPS = 0001111PPS = 0001111

00101000010100

11011011101101

10110011011001

01001000100100

00100010010001

Choose a Non Choose a Non Maxlength CAMaxlength CA


Overview of DesignCriterion for choosing Criterion for choosing

Non-Max Length CANon-Max Length CA• Large cycle of Large cycle of

length close to a length close to a Max length CycleMax length Cycle

• All members of PPS All members of PPS fall in smaller cyclesfall in smaller cycles

Target Cycle(TC)

Redundant Cycle(RC)

Choose a Non Choose a Non Maxlength CAMaxlength CA


Overview of DesignCriterion for choosing Criterion for choosing

Non-Max Length CANon-Max Length CA• Large cycle of Large cycle of

length close to a length close to a Max length CycleMax length Cycle

• All members of PPS All members of PPS fall in smaller cyclesfall in smaller cycles

Target Cycle(TC)

Redundant Cycle(RC)

In Practical In Practical Situation all Situation all members of PPS members of PPS don’t fall in RC.don’t fall in RC.

Then Sacrifice a Then Sacrifice a small part of TCsmall part of TC

Dmax


Design of TPG without PPS

•C1: Find n-cell CA having RCs and TC

•C2: Let most of the members of PPS fall in RC

•C3: Find Dmax in TC to avoid remaining PPSAcceptable Criteria•TC 2n-1 for n > 16

•TC .75 x 2n for n 16

•Dmax 10% of TC


Method of selecting RC

Design Simplification : Form CA with 2 RCs besides the all zero cycle

Value of RCs to form big TC

CA Size n 7

Divide n = n1 + n2 7

= 4 + 3

n1 and n2 are mutually

prime

Cycle Length RC1 = 2n1 –1

15

Cycle Length RC2 = 2n2 –1

7

Cycle Length TC = 2n1 –1 x

2n2 –1

105


Selection of n1 and n2• Each RC forms a vector subspaceEach RC forms a vector subspace• Evolve strategy to partition PPS in two Evolve strategy to partition PPS in two

vector subspacevector subspace• Randomly partition PPS into two sets S1 Randomly partition PPS into two sets S1

and S2 and S2 • Calculate rank of S1(r1) and S2(r2) Calculate rank of S1(r1) and S2(r2) • Select a partition where Select a partition where

– r1 + r2 r1 + r2 n n – r1 and r2 are mutually primer1 and r2 are mutually prime– The acceptable criterion of TC is metThe acceptable criterion of TC is met

• Set n1 = r1 and n2 = r2Set n1 = r1 and n2 = r2• T matrix can be designed with maximum T matrix can be designed with maximum

member of PPS falling in smaller cyclesmember of PPS falling in smaller cycles


Heuristic to Design the TPG

ProblemProblem

Since a CA forms a Band Matrix all linear Since a CA forms a Band Matrix all linear transform is not supported by CAtransform is not supported by CA

Randomly Synthesize a non-maximal length group CA

Method - illustrated in paper CA Toolkit - http://ppc.becs.ac.inMaximum member of PPS falls in RCs

•Find Dmax of rest of PPS covered by TC

•Select CA with acceptable criteria


Heuristic to Design the TPG

Acceptable CriteriaAcceptable Criteria

Dmax – 10% of TCDmax – 10% of TC

Randomly Synthesize a non-maximal length group CA

Method - illustrated in paper CA Toolkit - http://ppc.becs.ac.inMaximum member of PPS falls in RCs

•Find Dmax of rest of PPS covered by TC

•Select CA with acceptable criteria


Experimental Observation-I• Real data of PPS is not available• PPS randomly generated, no. of prohibited

patterns assumed 25• For a particular n, 10 different PPS are

considered

# Cell

PPS TC RCs PPS(%) in RCs

Dmax Avg # iteration

9 9 465 15, 31 75 48 25 14 15 8191 1,8191 95 106 23 24 25 223-1 1, 223-1 84 18121 14 32 25 * (215-1), (217-1) 89 33571 16 43 25 * (221-1), (222-1) 93 20211 15

* Indicates that the cycle length approx. 2n – 2n/2


Experimental Observations -II

Study of randomness property

Platform used is DiehardC

Compared with corresponding maximal length CA

Random TestRandom Test n=24n=24

Max TPGMax TPGn=32n=32

Max TPGMax TPGn=48n=48

Max TPGMax TPG

Overlap SumOverlap Sum pass passpass pass pass passpass pass pass passpass pass

3D Sphere3D Sphere pass passpass pass pass passpass pass fail failfail fail

B’day SpacingB’day Spacing fail failfail fail fail failfail fail fail failfail fail

Overlap 5-Overlap 5-permutpermut

fail failfail fail fail failfail fail pass passpass pass

DNADNA fail failfail fail fail failfail fail pass failpass fail

SqueezeSqueeze fail passfail pass fail failfail fail pass failpass fail


Experimental Observations -III

Fault coverage of the proposed design (Compared with MaxLength CA)

Fault Simulator used : Cadence `verifault’

Circuit Name

PI Test Vector Max Len TPG

C432m C499m C432

36 41 36

4000 2000 400

83.57 97.78 98.67

83.96 97.22 99.24

S641 S1269 S1196 S1238 S1423 S3384 S3271 S5378 S35932

35 18 14 14 17 43 26 35 35

2000 1200 12000 10000 15000 8000 10000 8000 14000

85.63 99.18 94.85 89.67 56.50 91.78 98.99 67.63 61.91

85.08 99.48 94.04 89.08 53.60 91.60 98.99 67.72 59.82


Conclusion

• Based on analytical framework of CA theory, the real life problem of PPS is addressed

• Solution does not incur extra overhead

• Fault efficiency of the TPG is as good as the existing designs

ASP-DAC/VLSI Design 2002 23

Thank youThank you

Niloy GangulyNiloy Ganguly

Documents

Niloy Ganguly Biplab K Sikdar P Pal Chaudhuri Presented by Niloy Ganguly Indian Institute of Social Welfare and Business Management. Calcutta 700 073 Email