AsyncSoc10_2

7/28/2019 AsyncSoc10_2

1/31

Self-Checking Circuits

Delay-Insensitive Codes

and

Self-Checking Checkers

7/28/2019 AsyncSoc10_2

2/31


Most important factors in designing a digital system:

Speed, Cost and Correctness.

Some systems used in

1. medical equipment used in ICUs,

2. aircraft control systems,

3. nuclear reactor control systems,

4. military systems and5. computing systems used in space missions.

High reliability is of the utmost importance.

DSM technology: Signal Integrity problem

7/28/2019 AsyncSoc10_2

3/31


Def: Self-Checking Circuit

Circuits detecting faults in normal operation.

Testing vs self-checking?

Faults: stuck at zero and stuck at one

stuck at one in one input of an 2-input OR gate?

stuck at zero in one input of an 2-input OR gate?

stuck at one in one input of an 2-input AND gate?

stuck at zero in one input of an 2-input AND gate?

7/28/2019 AsyncSoc10_2

4/31

Self-Checking Circuits:

Def: Error

An incorrect output caused by a stuck-at fault.

Def: Single Error

An error that affects only a single component value Def: Multiple Error

An error that affects multiple component values.

The component value affected by an error may

change form 0 to 1, or vice versa.

Def: unidirectional errors

When all components affected by a multiple error

change their values monotonically.

7/28/2019 AsyncSoc10_2

5/31


Def: Error Detecting Code

Y-Uy'andYyanderrorantoduey'y3.

words.noncodeofsettheis

andwordscodeofsettheis2.

vectors)ofuniversetheis(1.

U-Y

Y

UUY

Def: Hamming distance of two vectors x and y

the number of components in which they differ.

Def: Hamming distance of a code X

the minimum of the Hamming distances between all

possible pairs of code words in X.

7/28/2019 AsyncSoc10_2

6/31


Lemma: A code with Hamming distance d+1

can detect all errors with weight d or less.

Lemma: A code with Hamming distance 2c+1

can correct all errors with weight c or less. One-Hot Code:

1. Delay-Insensitive Code

2. Detect one error (H.D.=2).

7/28/2019 AsyncSoc10_2

7/31

Fault-tolerant Systems:

masking scheme:

1. All of the redundant modules are active at all times.

2. When a fault occurs, the faulty module is masked.

3. The most common masking scheme is

triple modular redundancy in which the outputs

of three copies of function units are fed to a

majority gate.

4. If one of the three modules becomes faulty,the two remaining fault-free modules mask the

results of the faulty one when the majority vote

is performed.

7/28/2019 AsyncSoc10_2

8/31

Fault-tolerant Systems:

Standby scheme:

1. only one copy of the system is active.

2. When the active module detects the occurrence

of faults, the standby module is activated and

takes over the control.3. Thus, to use self-checking circuits in a

fault-tolerant system, double module redundancy

is sufficient.

4. This scheme may be superior than the former

in terms of power consumption and hardware cost.

7/28/2019 AsyncSoc10_2

9/31

Self-checking scheme

Self-Checking scheme:

1. a self-checking functional unit.

2. a self-checking checker.

Self-Checking

functional unit

Self-checking

checker

... ... ...

...

Inputs

X

Outputs

Y

Error signal

X: input code space

Y: output code space

7/28/2019 AsyncSoc10_2

10/31


During the fault-free operation:

a normal input will produce a normal output.

If an incorrect output is produced due to a fault,

the error should be detected by the self-checkingchecker.

7/28/2019 AsyncSoc10_2

11/31


X}x)|{F(x,Y

),x(F

.)F(x,Xx

:

words)codeoutputthe(allspacecodeOutput5.

.:functionfree-faulta4.

:andfaultcontainingfunctiona3.

:infaulta2.

:faultsphsicalofsetthe1.

7/28/2019 AsyncSoc10_2

12/31


Fault Secure(FS):

code word input to a faulty circuit must not

produce an incorrect code word output.

Self-testing:

a fault in a circuit must be detected by some

input.

7/28/2019 AsyncSoc10_2

13/31


Fault Secure(FS):

Self-testing:

.or,ifonlyandif

torespectwithcallediscircuitA

)F(x,)F(x,Y)F(x,Xx

uresecfault-

.,

ifonlyandiftorespectwithcallediscircuitA

Y)F(x,Xx

ngself-testi

7/28/2019 AsyncSoc10_2

14/31


Totally Self-Checking:

Partially Self-Checking:

.torespectwithandisitifonlyandif

torespectwith(TSC)callediscircuitA

uresecfault-ngself-testi

glf-checkintotally se

.subsetaforandforisit

ifonlyandif

torespectwithcallediscircuitA

XIuresecfault-Xngself-testi

ingself-checkpartially

7/28/2019 AsyncSoc10_2

15/31


Fault-secure-only circuits:

1. No erroneous results go undetected.

2. However, it is possible that some fault can

never be detected.

Self-testing-only circuit:

1. Any fault can produce undetected errors for a

short time.2. However, there is a code word input that can

detect the fault.

7/28/2019 AsyncSoc10_2

16/31


Totally self-checking circuit:

1. no erroneous results go undetected and

2. any fault will be eventually detected.

Partially self-checking circuits:

1. This approach is to restrict the set of faults for

which the circuit has to be checked.

2. They are introduced to provide low-cost errordetection.

3. They may be used in non-critical applications.

7/28/2019 AsyncSoc10_2

17/31

Delay-Insensitive Tree Adder

7/28/2019 AsyncSoc10_2

18/31

Self-Checking Checkers

.,and,

ifonlyandifcallediscircuitA

Y)F(x,XxY)F(x,Xx

intdisjocode

Code-disjoint:

TSC Checker:

.torespectwithdisjoint-codeandsecure-faulttesting,-selfisitifonlyandif

torespectwithcheckerTSCacallediscircuitA

With the code-disjoint feature, one may be able to

test if the TSC checker is malfunction.

7/28/2019 AsyncSoc10_2

19/31

DI Adder Checker

Code word input: one-hot code of output signals(adder)

Correct code word output Z0 Z1 = 10

Incorrect code word outputs Z0 Z1 = {00 01 11}

7/28/2019 AsyncSoc10_2

20/31


M/N code (M

7/28/2019 AsyncSoc10_2

21/31

Delay-Insensitive

Transmission

I I

encoder decoder

DI codes

Sender Receiver

7/28/2019 AsyncSoc10_2

22/31

Delay-Insensitive

Transmission

Cost factors:

1. Number of Wires (cost)

2. Encoder (logic complexity/computation time)3. Decoder (logic complexity/computation time)

7/28/2019 AsyncSoc10_2

23/31

Delay-Insensitive Codes:

Berger

Berger Code:

1. Systematic code: Information bits + Check bits

(note that M/N code is a nonsystematic code).

2.

3. Check bits = counting the number of 0s in I bits

4. See table (Next page)

1logIbitsnInformatioandKbitsCheck

2

IK

7/28/2019 AsyncSoc10_2

24/31


Systematic Non-sysN Info

bit 2-rail Berger 3/6 code

0 0000 1111 100 0001111 0001 1110 011 001011

2 0010 1101 011 001101

3 0011 1100 010 001110

4 0100 1011 011 010011

5. ...

7/28/2019 AsyncSoc10_2

25/31

Delay-Insensitive

Transmission: Berger codes

I

I

Check

bits

DI codes

Sender Receiver

Check

bits

CCC

Compare

Valid?

7/28/2019 AsyncSoc10_2

26/31

Self-Checking Checkers:

Self-checking Checkers of M/N code

1. One-hot code(1/N code):

a. dual-rail encoding: (01 10):

shown in DI Addersb. 1/N code:

c. Z0: completion signal

Z1: error detection&

+

& &...

C(N,2)

+...

Z0 Z1

7/28/2019 AsyncSoc10_2

27/31


Self-checking Checkers of M/N code

2. Optimal M/N code: M=N/2

a. 3/6 code: (000111,001011,001101,001110,

b. length of M/N Code = C(N, N/2)

&

+

& &...

C(N,n/2+1)

Z1

&

+

& &...

C(N,N/2)

Z0

N/2..

N/2+1..

7/28/2019 AsyncSoc10_2

28/31


Use Sorting Networks for Self-checking Checkers:

General sorting network:

Sorting

Network... ...

A1

An

Max(A1, ,An)

Min(A1, ,An)

nunsortednumbers

nsorted

numbers

ComparatorA1

A2

Max(A1,A2)

Min(A1,A2)

7/28/2019 AsyncSoc10_2

29/31


Binary sorting network:

SortingNetwork

...

...

x1

xn

1 k 1s

10 n-k os

0

nbinaryinput

Comparatorx1

x2

Max(x1,x2)= x1+x2

Min(x1, x2)= x1x2

...

7/28/2019 AsyncSoc10_2

30/31


Binary sorting network for 2/4 code

CMP

CMP

CMP

CMP

CMP

7/28/2019 AsyncSoc10_2

31/31

Error Collection Codes:

Code with HD>=3 may correct error

Ex. HD=4: 0011 1100

Date post:	03-Apr-2018
Category:	Documents
Upload:	ramanaidu1
View:	216 times
Download:	0 times

AsyncSoc10_2

Documents