Fault-Tolerant Computing - Assignment | ECE 257A, Assignments of Electrical and Electronics Engineering

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Nov. 2007

Reconfiguration and Voting

Slide 1

Fault-Tolerant Computing^ HardwareDesignMethods

Nov. 2007

Reconfiguration and Voting

Slide 2

About This Presentation Edition^

Released

Revised

Revised

First^

Nov. 2006

Nov. 2007

This presentation has been prepared for the graduatecourse ECE 257A (Fault-Tolerant Computing) byBehrooz Parhami, Professor of Electrical and ComputerEngineering at University of California, Santa Barbara.The material contained herein can be used freely inclassroom teaching or any other educational setting.Unauthorized uses are prohibited. © Behrooz Parhami

Nov. 2007

Reconfiguration and Voting

Slide 4

Nov. 2007

Reconfiguration and Voting

Slide 5

Multilevel Model of Dependable Computing

Component

Logic

Service

Result

Information

System

Level^ →

Low-Level Impaired

Mid-Level Impaired

High-Level Impaired

Unimpaired

Entry Legend:

Deviation

Remedy

Tolerance

Ideal

Defective

Faulty

Erroneous

Malfunctioning

Degraded

Failed

Nov. 2007

Reconfiguration and Voting

Slide 7

Reconfiguration via Programmable Connections^ Interconnectionswitch with 4 ports(horizontal lines)and 3 channels^ (vertical lines)^ Each port can beconnected to 2 ofthe 3 channels

1

1

2

2

If each module port were connected to every channel, the maximumflexibility would result (leads to complex hardware & control, though) The challenge lies in using more limited connections effectively

Nov. 2007

Reconfiguration and Voting

Slide 8

Multiple-Bus Multiprocessors

Failed units can be isolatedfrom the buses No single bus failure canisolate a module from the rest of the system

The vertical channels may be viewed as buses and theheavy dots as controllable bus connections, making thismethod applicable to fault-tolerant multiprocessors

Write enable Read / Writedata

QFFWrite path Read path Connection FF

Bus

If we have extra buses, thenfailure in the bus connectionlogic can be tolerated byavoiding the particular bus For reliability analysis, lump thefailure rate of reconfiguration logicwith that of its associated bus

Nov. 2007

Reconfiguration and Voting

Slide 10

Choosing the Rows/Columns to Bypass

In the adjacent diagram, can wechoose up to 2 rows and 2 columnsso that they contain all the faults?

Sparecolumns

Sparerows

Rowswithfaults^0236

Columnswithfaults^01357 0 3

1 7

Question: In a large array, with

r^ spare rows and

c^ spare

columns, what is the smallest number of faults that cannotbe reconfigured around with row/column bypassing?

Convert to graph problem (Kuo-Fuchs): Form bipartite graph, with nodes corresponding to faulty rows and columns Find a cover for the bipartite graph (set of nodes that touch every edge)

Nov. 2007

Reconfiguration and Voting

Slide 11

Switch Modules in FPGAs

Interconnection switchwith 8 ports and fourconnection choices foreach port: 0 – No connection 1 – Straight through 2 – Right turn 3 – Left turn 8 control bits (why?)

(^21)

1 2

3

3

(^454)

5

(^88)

7 6

6 7

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Reconfiguration and Voting

Slide 13

One-Track and Two-Track Switching Schemes^ One-track switching model

Two-track switching model

Source: S.-Y. Kung, S.-N. Jean, C.-W. Chang,

IEEE TC

, Vol. 38, pp. 501-514, April 1989

Nov. 2007

Reconfiguration and Voting

Slide 14

Voting and Its Role in Dependable Computing^ John von Neumann, 1956: “Probabilistic Logic and Synthesis ofReliable Organisms from Unreliable Components”^ Hardware voters for multichannel computation^ Voting schemes in these three contexts share some propertiesGeneral schemes have been devised to cover all these instances

High performance (pipelined) Software voters for multiversion programmingImprecise results (approximate voting) Consistency of replicated data Weighted voting and weight assignment

Nov. 2007

Reconfiguration and Voting

Slide 16

There is More to Voting than Simple Majority Plurality voting: Select the value that appearson the largest number of inputs Example:

vote(1, 3, 2, 3, 4) = 3 What should we take as the result of vote(1.00, 3.00, 0.99, 3.00, 1.01)?

x^1 x^2^...^ xn

Pluralityvoter

y

It would be reasonable to take 1.00 as the result, because 3 inputsagree or approximately agree with 1.00, while only 2 agree with 3.00 Will discuss approximate voting and a number of other sophisticatedvoting schemes under software design topics Median voting: one way to deal with approximate values median(1.00, 3.00, 0.99, 3.00, 1.01) = 1.01 Median value is equal to the majority value when we have majority

Nov. 2007

Reconfiguration and Voting

Slide 17

Threshold Voting and Its Generalizations Simple threshold (

m -out-of-

n ) voting:

Output is 1 if at least

m^ of the

n^ inputs are 1s

Majority voting is a special case of thresholdvoting: (

⎣ n /2⎦^

• 1)-out-of-

n^ voting

Agreement or quorum sets { x ,^ x^1

}, { x 2 2 ,^ x }, { 3

x ,^ x^3

} – same as 2-out-of-

{ x ,^ x^1

}, { x 2 1 ,^ x ,^ x 3

}, { x 4 2 ,^ x ,^ x 3

Weighted threshold (

w -out-of-

Σ v^ ) voting: i^

Output is 1 if

Σ v^ x^ i^ i^

is^ w^ or more

x^1 x^2^...^ xn

m Threshold gate

y

x^1 x^2^...^ xn

w Threshold gate

y v^1 v 2^ v^ n

The 2

nd^ example above is weighted voting with v =^ v^1

= 2,^2

v =^ v^3

= 1, and threshold 4

w^ = 4

Agreement sets are more general than weighted voting in the sense ofsome agreement sets not being realizable as weighted voting

Nov. 2007

Reconfiguration and Voting

Slide 19

Implementing Weighted Threshold Voters Example:

Implement a 4-input threshold voter with^ v

=^ v 1 2 = 2,^ v

=^ v 3 4 = 1, and threshold

w^ = 4

Strategy 1:

If weights are small integers, fan-out each input an appropriate numberof times and use a simple threshold voter

x^1 x (^2) x^3^ x^4

4 Threshold gate

y

Strategy 3:

Convert the problem to agreement sets (discussed next) Strategy 2:

Use table lookup based on comparison results x = x^1

x = x^1

x = x^2

x = x^3

Result

x^

x^

x^

x^1

Error

x^1

x^2

x^

x^

Error

Is this table complete?Why, or why not?

Nov. 2007

Reconfiguration and Voting

Slide 20

Implementing Agreement-Set Voters

Example:

Implement a voter corresponding to the agreement sets { x ,^ x^1

}, { x 2 1 ,^ x ,^ x 3

}, { x 4 2 ,^ x ,^ x 3

Strategy 1:

Implement as weighted threshold voter, if possible Strategy 2:

Implement directly Find a minimal set of comparators that determine the agreement set

Complete this designby producing the“no agreement” signal

x = x^1 2 x = x^1 3 x = x^3 4 x = x^2

x^2 x^1

0 1

y