data communication slide on data rate and efficiency

data communication slide on data rate and efficiency

1. DATA RATE
Prepared by
Nusrat Chowdhury
Assistant Professor, Department of EEE

2. Lecture Contents
Noiseless Channel: Nyquist Bit Rate
Noisy Channel: Shannon Capacity
Using Both Limits

3. DATA RATE LIMITS
Averyimportantconsiderationindata
communicationsishowfastwecansenddata,inbits
persecond,overachannel.Dataratedependson
threefactors:
1.Thebandwidthavailable
2.Thelevelofthesignalsweuse
3.Thequalityofthechannel(thelevelofnoise)

4. Nyquist Theorem
Nyquistgivestheupperboundforthebitrateofa
transmissionsystembycalculatingthebitrate
directlyfromthenumberofbitsinasymbol(or
signallevels)andthebandwidthofthesystem
(assuming2symbols/percycleandfirst
harmonic).
Nyquisttheoremstatesthatforanoiseless
channel:
C=2Blog
22
n
=2Blog
2L
C=capacityinbps
B=bandwidthinHz

5. Consideranoiselesschannelwithabandwidthof3000
Hztransmittingasignalwithtwosignallevels(foreach
level,wesend1bits).Calculatethemaximumbitrate.
Example 3.34
We know for noiseless channel , Channel capacity or bit rate should be calculated
using the formula below:

6. Example3.36
Weneedtosend265kbpsoveranoiselesschannel
withabandwidthof20kHz.Howmanysignallevels
doweneed?Commentonyouranswer.

7. Weneedtosend265kbpsoveranoiselesschannelwith
abandwidthof20kHz.Howmanysignallevelsdowe
need?Commentonyouranswer.
Solution
WecanusetheNyquistformulaasshown:
Example 3.36
L=2^(C/2B)
This is not a valid number. So possible values of n= 6 or 7
If n=6 then L=64, and C= 240 kbps
and if n=7 then L=128, C= 280kbps

8. Shannon’s Theorem
Shannon’s theorem gives the capacity of a
system in the presence of noise.
C = B log
2(1 + SNR)

9. Consideranextremelynoisychannelinwhichthevalue
ofthesignal-to-noiseratioisalmostzero.Inother
words,thenoiseissostrongthatthesignalisfaint.For
thischannelthecalculatethecapacity.
Example 3.37
Thismeansthatthecapacityofthischanneliszero
regardlessofthebandwidth.Inotherwords,wecannot
receiveanydatathroughthischannel.

10. Wecancalculatethetheoreticalhighestbitrateofa
regulartelephoneline.Atelephonelinenormallyhasa
bandwidthof3000.Thesignal-to-noiseratioisusually
3162.Forthischannelcalculatethechannelcapacity.
Example 3.38
Thismeansthatthehighestbitrateforatelephoneline
is34.860kbps.Ifwewanttosenddatafasterthanthis,
wecaneitherincreasethebandwidthofthelineor
improvethesignal-to-noiseratio.

11. Example3.39
Thesignal-to-noiseratioisoftengivenindecibels.
AssumethatSNR
dB=36andthechannelbandwidthis
2MHz.Calculatethechannelcapacity.

12. Thesignal-to-noiseratioisoftengivenindecibels.
AssumethatSNR
dB=36andthechannelbandwidthis2
MHz.Calculatethechannelcapacity.
Example 3.39

13. Forpracticalpurposes,whentheSNRisveryhigh,we
canassumethatSNR+1isalmostthesameasSNR.In
thesecases,thetheoreticalchannelcapacitycanbe
simplifiedto
Example 3.40
Forexample,wecancalculatethetheoreticalcapacityof
thepreviousexampleas

14. Example3.41
Wehaveachannelwitha1-MHzbandwidth.The
SNRforthischannelis63.Whataretheappropriate
bitrateandsignallevel?

15. Wehaveachannelwitha1-MHzbandwidth.TheSNR
forthischannelis63.Whataretheappropriatebitrate
andsignallevel?
Solution
First,weusetheShannonformulatofindtheupper
limit.
Example 3.41
L=2^(C/2B)

16. TheShannonformulagivesus6Mbps,theupperlimit.
Forbetterperformancewechoosesomethinglower,4
Mbps,forexample.ThenweusetheNyquistformulato
findthenumberofsignallevels.
Example 3.41 (continued)

17. The Shannon capacity gives us the
upper limit; the Nyquist formula tells us
how many signal levels we need.
Note

18. Practice Problem

19. Example 3.18
Assumeweneedtodownloadtextdocumentsattherate
of100pagesperminute.Whatistherequiredbitrateof
thechannel?Considereachpagecontains24linesand
eachlinecontains30letters.

21. Example 3.20
Whatisthebitrateforhigh-definitionTV(HDTV)?TheHDTV
Screenisnormallyaratioof16:9.Thereare1920by1080pixels
perscreen,andthescreenisrenewed30timespersecond.
Twenty-fourbitsrepresentsonecolorpixel.

23. Q.3.Wehaveachannelwith4.5kHzbandwidth.Ifwewantto
senddataat120Kbps,whatistheminimumSNRdB?Whatis
SNR?Alsocalculatetheno.oflevels.