Error Correction and Flow Control

Martin Weiss

Slide 2

Objectives of this Meeting

Describe different flow control techniques

Describe the major error detection techniques

Slide 3

Review of the Last Meeting

Error detection Forward error correction

Slide 4

Error Correction Automatic Response Request

(ARQ) Forward error correction

Slide 5

Types of ARQ

Stop-and-Wait (Idle RQ) Sliding Window (Continuous RQ)

Slide 6

Stop and Wait

1 Data 0

2 ACK0

3 Data 1

4 NACK1

5 Data 1

6 ACK1

7 Data 0

Slide 7

Stop and Wait (Long Channel)

1 Data 0

2 ACK0

3 Data 1

4 ACK1

Increasing bit rate

1 D 0

2 A0

3 D 1

4 A1

Slide 8

Performance of Stop and Wait

t=0

t=tp

t=tt

t=tt+tp

t= x+tt+tp

t= x+ta+tt+tp

t= x+ta+tt+2tp

Slide 9

Performance of Stop and Wait

Error free (assume ta << tt and x=0)

att

tU

tp

t

21

1

2

Slide 10

Error Calculations

How many frames are transmitted for a frame to be properly received?– This is a probability distribution– Assuming independence of errors,

– The mean of this is a geometric dist.

)1(}ions transmissPr{ 1 PPj j

PPjPN

j

j

1

1)1(

1

1

Slide 11

Error Calculations P is the probability of frame error This can be estimated using:

– p is the bit error rate– k is the number of bits per frame

Using burst error rate is more accurate You can assume that the burst error

rate = 1/3 bit error rate

kpP )1(1

Slide 12

Stop and Wait with Errors

The error-free throughput is

Since it takes an average of NT frames to get an error free one, we can compute:

a

RT

21

a

PR

Na

RT

T 21

)1(1

21

a

P

R

TU

21

1

Slide 13

Sliding Window

Transmitter may transmit several messages before awaiting response

The number of unacknowledged messages permitted is the Window Size

Slide 14

Sliding Window (n>3)

0 Data 0

1 Data 1

2 Data 2

3 ACK 20

Slide 15

Sliding Window (Go-Back-N)

4 Data 4

5 Data 5

6 Data 6

7 NACK 41

8 Data 4

9 Data 5

10 Data 6

Slide 16

Performance of Sliding Window Protocols

Error-free (Go-Back-N and Selective Repeat)

12

21

121

aNa

NaN

U

Slide 17

Selective Repeat with Errors

If N is large enough, only the errored frames are retransmitted (occurring at a rate of (1-P)

Thus, the utilization becomes

12

21

1121

aNa

PNaNP

U

Slide 18

Go-Back-N with Errors

The number of retransmitted frames is

– When– Notice that when

»N>(2a+1) then»N<(2a+1) then K=N

P

KPPPPifN

i

ir

1

1)1(

1

1

KiKKiif )1()1(1

12 aK

Slide 19

Go-Back-N with Errors

For N>2a+1 For N<2a+1

Substituting and simplifying, we obtain:

12

121

1

1221

1

aNNPPa

PN

aNaP

P

U

rNU

1

)12(

aN

NU

r

Slide 20

Performance IssuesU

0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000a

Sliding Window(N=7)Stop and

Wait

P=10-3

Slide 21

Comparing Sliding Window Approaches

Selective Reject Go-Back-N

Slide 22

Types of Protocols

Byte-oriented protocols Bit-oriented protocols

Slide 23

Protocol Environments End-to-End Local

Slide 24

Structure of Byte-Oriented Protocols

SYN SYN SYN HeaderSOH STX Message EOT

Sample Structure

SYN = SynchronizationSOH = Start of HeaderSTX = Start of TextEOT = End of Text

Slide 25

Structure of Bit-Oriented Protocols

Preamble Flag Header Message Trailer Flag

Sample Frame Structure

Preamble: Used for Bit SynchronizationFlag: Identifies Start and End of MessageTrailer: Error Checking

Slide 26

Bit Stuffing

Example

0100101111010101101110000010111110010101111110

Transmission Direction

Locations for Stuff Bits

010010111101010110111000001011111000101011111010

Original Bit Stream

Transmitted Bit Stream

Slide 27

Design of Transmitter and Receiver

Application

NetworkSoftware

Bit Stuffing Flag Insertion

Control

Transmitter Receiver

Application

NetworkSoftware

Bit Destuffing

Control

Flag Detection