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E303 & ISE3.2E IMPERIAL COLLEGE LONDON, DEPARTMENT of ELECTRICAL and ELECTRONIC ENGINEERING. COMPACT LECTURE NOTES on COMMUNICATION THEORY. Professor Athanassios Manikas, (revised Autumn 2008) PCM and PSTN (Public Switched Telephone Network) Outline: ì PCM: Bandwidth, Bandwidth Expansion Factor, Quantization, output SNR and Threshold Effects, Differential PCM. ì CCITT recommendations for PCM (24-channels and 30-channels) ì Plesiochronous digital hierarchies (PDH) ì Synchronous digital hierarchies (SONET/SDH)
Transcript

E303 & ISE3.2E

IMPERIAL COLLEGE LONDON,DEPARTMENT of ELECTRICAL and ELECTRONIC ENGINEERING.

COMPACT LECTURE NOTES on COMMUNICATION THEORY.Professor Athanassios Manikas, (revised Autumn 2008)

PCM

and

PSTN(Public Switched Telephone Network)

Outline:

ì PCM: Bandwidth, Bandwidth Expansion Factor, Quantization, output SNRand Threshold Effects, Differential PCM.

ì CCITT recommendations for PCM (24-channels and 30-channels)ì Plesiochronous digital hierarchies (PDH)ì Synchronous digital hierarchies (SONET/SDH)

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 2 Prof. A. Manikas

1. INTRODUCTION

Channel Encoder

Discrete ChannelEncoder

Interleaver

Discrete channel

Channel Decoder

Discrete ChannelDecoder

DeInterleaver

DigitalModulator(M , Tcs)

rcs=1/Tcs bauds

EUEBUESNIRin

DigitalDemodulator(M , Tcs)

DecoderSource

-Fg

1

+Fgf

pe=f( )EUE

LPF

g (t)0n (t)0

SNRout pe=f( )

Con t.Info Sink

g(t)

Sampler ( )Fs

Quantizer ( )Q , Δ

N.B.:Fs>2Fg

EncoderSourceCon t.

Info Source

Ana

logu

e C

HA

NN

EL

k

(B ,C)

+ n (t)i

1B

f

B

H( )f^ ^ ^

^^ ^

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 3 Prof. A. Manikas

ì œ of an analogue signal are transmittedPCM sampled quantized valuesvia a .sequence of codewords

i.e. after sampling & quantization, a is used to map theSource Encoderquantized levels (i.e. o/p of quantizer) to codewords of bits#

i.e. quantized level codeword of bitsÈ #

and, then, a digital modulator is used to trasmit the bits,i.e. PCM system

ì There are three popular PCM source encoders(or, in other words, Quantization-levels Encoders).

Binary Coded Decimal (BCD) source encoder Folded BCD source encoder Gray Code (GC) source encoder

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 4 Prof. A. Manikas

000011010

001010011

010001001

011000000

100100100

101101101

110110111

111111110

m1

m2

m3m4

m5

m6

m7m8 BCD code

Folded BCDGRAY Code

g q (Volts)

g (Volts)

g g(input outputÑ È Ð Ñq

g F q ssamples

sec: occurs at a rate N.B.: F .FÐ   # Ñs g

U œ quantizer levels;

#= log# U ,3>=level

ì :Note

codeword rate ( ) quant levels rate sampling rate = o/p of source encoder

Å Å Å#-bit

seclevels

sec sec-9./A9<.= =+7:6/=

= = =Þ J #J= 1

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 5 Prof. A. Manikas

ì U œ bit rate: e.g. for 16 levels then r = . r = . b b

bitslevel

levelssec

bitssec#

J % JÅ Å= =

(e.g. transmitted sequ.=101011001101 ....)Æ Æ

Å

ì

Å

versions :of PCM

Differential PCM (DPCM): diff. quantizersDelta Modulation: diff. quants with 2 levels + or

a

ÚÝÝÝÝÝÝÛÝÝÝÝÝÝÜ

? ?

re encoded using a single binary digit

(DM DPCM)Others

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 6 Prof. A. Manikas

2. PCM: BANDWIDTH & "ì we transmit several digits for each quantizer's output level Ê F PCM g F

where denotes the channel bandwidthrepresents the message bandwidthœFPCM

g

F

ì PCM Bandwidth

baseband bandwidth: F  PCMchannel symbol rate

2 Hz

bandpass bandwidth: HzF  PCMchannel symbol rate

2 2 ‚

ì Note that, by default, the Lower bound of the 'baseband' bandwidth isassumed and used in this course

ì bandwidth expansion factor œ œ" channel bandwidthmessage bandwidth

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 7 Prof. A. Manikas

ì Example - Binary PCM

F œ Ê FPCM PCM2 2channel symbol rate bit rateœ œ œ J œ J

ÅU

#J#

#

1 1= # #

log

Hz

F Ê œ Ê œPCM œ J# 1 FJPCM1

# " #

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 8 Prof. A. Manikas

3. The Quantization Process ( 2)output point-A• at point A2:a signal discrete in amplitude and discrete in time.

The blocks upto the point A2, combined, can be consideredas a discrete information source where a discrete messageat its output is a "level" selected from the output levels ofthe quantizer.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 9 Prof. A. Manikas

• analogue samples finite set of levelsÈ

where the symbol denotes a "map"È

In our case this is called mapping quantizing

i.e.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 10 Prof. A. Manikas

• quantizer parameters:

ÚÝÝÝÝÝÛÝÝÝÝÝÜ

U,

ÀÀ 3 œ U

Ð Ñà

number of levelsinput levels of the quantizer, with 0,1,...., known as quantizer's

3

b =lowest level! outputs levels of the quantizer sampled values after quantization with 1,...., ; known as

end-points

output-levels7

<?6/

3 À Ð Ñ3 œ U

À connects the input of the quantizer to m3

RULE:

the sampled values of an analogue signal are converted to oneg kT g t Ð Ñ Ð Ñsof allowable output-levels according to the rule:Q m , m ,..., m " # Q

g kT m or equivalently g kT =m Ð Ñ Ð Ð Ñ Ñs q sÈ 3 3

with iff b g kT b b = , b =+ ,3" 3 !Ÿ Ÿ ∞ ∞Ð Ñs Q

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 11 Prof. A. Manikas

• quantization noise at each sample instance:

8 Ð5X Ñ œ Ð Ñ Ð Ñ; = g kT g kT; s s s

If the power of the quantization noise is small,

i.e. = =small, P8;X˜ ™8 Ð5X Ñ2

; =

then the quantized signal i.e. signal at the output of the quantizer is aÐ Ñgood approximation of the original signal.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 12 Prof. A. Manikas

• quality of approximation may be improved by careful choice of 's andb3m3's and such as a measure of performance is optimized.

e.g. measure of performance: Signal to quantization Noise power RatioÐ Ñnotation: SNRq

SNRq = =signal powerquant. noise power

TT

1

8;

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 13 Prof. A. Manikas

• Types of quantization:

uniformnon-uniform

differential =

ÚÝÝÛÝÝÜ œ

uniform, or non-uniform, plus a differential circui>

• Transfer Function:uniform quantizer non-uniform quantizer

for signals with for signals with CF=small CF=large

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 14 Prof. A. Manikas

The following figure illustrates the main characteristics of different types of quantizers

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 15 Prof. A. Manikas

3.1. UNIFORM QUANTIZERS

• Uniform quantizers are appropriate for uncorrelated samples

g t g kTÐ Ñ Ð Ñ{ }q s

{ }g kT

uncorrelated

Ð ÑÅ

s

• g kT g g kT glet us change our notation: to and to q s q sÐ Ñ Ð Ñ• the range of the continuous random variable is divided into intervalsg Qof equal length ?

• value of midpoint of the quantizing interval in which the value of fallsÐ Ñ Ð Ñg gÈ

or equivalently for 1,2,.., 1m = 3#

b b3" 3 3 œ U Ð Ñ

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 16 Prof. A. Manikas

• step size: 2? œb b

QQ ! Ð Ñ

• g =m b g b b = b + .m =rule: iff where 3q - b +b3 3 " 33 !

3 #

Ÿ3œ ?

3 " 3- Ð Ñ

for 1,2,..,3 œ U

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 17 Prof. A. Manikas

COMMENTS ON UNIFORM QUANTIZER

ˆ U œ Ê Since, in general, large P P gg gq ¶ ´ Xe f#ˆ U œ Å Ð Ñ Furthermore, large implies that Fidelity of Quantizer g qq ¶

ˆ U ) "'= - are just sufficient for good intelligibility of speech;

Ð Ñbut quantizing noise can be easily heard at the background voice telephony: minimum ; i.e. SNR 42dB128 levels Ð ¶ Ñq

N.B.: 128 levels 7-bits to represent each levelÊ transmission bandwidth =Ê Å

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 18 Prof. A. Manikas

ˆ Ð Ñif then 2 4 Quantizer=UNIFORM pdf of the input signal=UNIFORMœ SNR Q =q œ # ##

ˆ Ð Ñ Quantization Noise Power: 5P =n

q?#

"#

ˆ œ Ð Ñ rms value of Quant.Noise=fixed= 6/?È12fe fg

.. g t =small SNR. if for extended period of time the design value

this phenomenon is obviousif the signal waveform hasa lar

Ð Ñ Ê Å

q

ge

7

CREST FACTOR

Ð Ñ

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 19 Prof. A. Manikas

ˆ Ð Ñ 8remember: CREST FACTOR ´ peak rms

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 20 Prof. A. Manikas

ˆ ÆÅ

By using CREST FACTOR effects=variable spacing

small spacing near 0 and large spacing at the extremes

Ê

and this leads to NON-UNIFORM QUANTIZERS

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 21 Prof. A. Manikas

3.2. NON-UNIFORM QUANTIZERS• Non-Uniform quantizers are like unif. quants appropriateÐ Ñfor uncorrelated samples

g t g kTÐ Ñ Ð Ñ{ }q s

{ }g kT

uncorrelated

Ð ÑÅ

s

• step size = variable Ð Ñ?3

• pdf uniformif i/p Áthen non-uniform quantizers yield higher SNR than uniform quantizersq

• rms value of is not constant but depends on the sampled value n g kTq sÐ Ñof g tÐ Ñ

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 22 Prof. A. Manikas

• iff rule: g =m b g bq -3 3 " 3 Ÿ

where b = , b =+ =b b =variable! 3 3 3"∞ ∞ Q ?

• example:

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 23 Prof. A. Manikas

max(SNR) NON-UNIFORM QUANTIZERS

b , m SNR3 3 are chosen to maximize as follows:q

since Q=large P P g SNR =max P =minÊ ¶ ´ Êg g q nq qXe f# if

where pdf P = g m . . dgn g

Q

=b

bq i-

i'3 "

3#

"Ð Ñ

Therefore 9 Pm ,bmin3 3

nq Ð Ñ

Ð Ñ Ð Ñ9 is equivalent to the following two equations: 10ÚÛÜ

dPdb

dPdm

nq

nq

4

4

= 0

=0

Ê " # U "

# " # U

Ð Ñ Ð Ñ Ð Ñ Ð Ñ

Ð Ñ Ð Ñ

b m . b b m . b =0 j= , ,..., . g m . g .dg=0 j= , ,...,

4 4 4 4 4 " 4# #

4

pdf pdf forpdf for

g + g

bb

gj-

j

"' 11Ð Ñ

In the second branch of Equation-11 the parameter m can be seen as the4

statistical mean of the j quantizer interval>2

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 24 Prof. A. Manikas

Note:

the above set of equations i.e. 11 cannot be solved in for aÐ Ð ÑÑ closed formgeneral pdf. Therefore for a specific pdf an appropriate method is givenbelow in a step-form:

METHOD:

1. choose a m"

2. calculate s, 'sb ' m3 3

3. check if is the mean of the interval m b , Q Q-c d" ∞ if yes STOPÄ else choose a new and then goto 2Ä Ð Ñm "

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 25 Prof. A. Manikas

A SPECIAL CASE:max(SNR) Non-Uniform Quantizer of a Gaussian Input Signal

if the input signal has a Gaussian amplitude pdf, that is, pdf = 0, g g 5Ð Ñthen it can be proved that:

2.2 12P = Q

not easy to derive

n g.

q 5# " *'

Å

Ð Ñ

In this case the Signal-to-quantization Noise Ratio becomes:

SNR 13qPP Q

. = = = Q gq g

nq g.

5

5

#

# " *'#Þ#" *'!Þ%& Ð Ñ

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 26 Prof. A. Manikas

Compander's type non-uniform quantizers (performance independent of CF)• NON-UNIFORM QUANTIZER ..´

+ SAMPLE SAMPLECOMPRESSION EXPANDER

UNIFORMQUANTIZER´

• COMPRESSOR EXPANDER+ ´ COMPANDER

g g . g = g =uniform gmeans

"such that"

È Èf ffc c g ci.e pdfš › À

Åc

-"

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 27 Prof. A. Manikas

• Popular companders: use compressionlog

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 28 Prof. A. Manikas

• ATwo compression rules ( -law and -law) which are used in PSTN and.provide a SNRq independent of signal statistics are given below:

-law (USA) -law (EUROPE). A

• A In practice œ ¶ )(Þ'¶ "!!.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 29 Prof. A. Manikas

• Compression-Rules (PCM systems).-law A-law

g = g g.g 0

c max c

+ .

+

. max

gg

ln

ln

ln

ln

Š ‹Š ‹

Š ‹Š

" ± ±

"

± ± "

.

.

ggmax

ggmax

max

œ

Ÿ ÚÝÝÛÝÝÜ

½ ½A

A A1+

1+ A

A A.

maxg

g± ±

"g

gmax

max

‹Š ‹1+ln

g Ÿ "½ ½where

gc= compressor's output signal (i.e. input to uniform quantizer)

g= compressor's input signal

g gmax=maximum value of the signal

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 30 Prof. A. Manikas

The 6dB LAW

uniform quantizer: SNR CF ; œ %Þ(( ' #!# log dB remember =CF :/+5

<7=

.-law: SNR; œ %Þ(( ' #! "# .log ln dB

E-law: SNR; œ %Þ(( ' #! " E# log ln dB

A or lawμ Uniform quantizer

SNRq (dB)

CF

Uniform quantizer

CF

γ bits

γ+1 bits6dB

SNRq (dB) SNRq (dB)

CF

A or lawμ

γ+1 bits

γ bits6dB

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 31 Prof. A. Manikas

• REMEMBER the following figure (illustrates the main characteristics of different types of quantizers)

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 32 Prof. A. Manikas

COMMENTS

• uniform & non-uniform quantizers:

use them when samples are uncorrelated with each other i.e. the sequenceÐis quantized independently of the values of the preceding samples Ñ

• practical situation:

the sequence { constists of samples which are correlated with eachg kT Ð Ñs ×other. In such a case use differential quantizer.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 33 Prof. A. Manikas

• Examples:

PSTN kHz, Q=2 (A=87.6 or =100) bits levelJ œ ) ß œ ) Î=

) . #

i.e. bit rate: 8k 8 64 kbits/sec< œ J ‚ œ ‚ œ, = #

Mobile - GSM

kHz, Q=2 bits level,J œ ) ?8309<7 Ê œ "$ Î="$ #

i.e. bit rate: 8k 13 104 kbits/sec< œ J ‚ œ ‚ œ, = #

which, with a differential circuit, is reduced to <,=13kbits/sec

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 34 Prof. A. Manikas

3.3. DIFFERENTIAL QUANTIZERS

• Differential quantizers are appropriate for correlated samplesnamely they take into account the sample to sample correlation inthe quantizing process;

• e.g. Transmitter (Tx) Receiver (Rx)

PredictorW W

38:?>Î ÑÏ Ò

currentmessagesymbol

• The weights are estimated based on the autocorr function of the inputA Þ• . Therefore, the Tx transmitsThe Tx & Rx predictors should be identicalalso its weights to the Rx (i.e. weights are transmitted together with theAdata)

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 35 Prof. A. Manikas

• g kT d kTIn practice, the variable being quantized is not but the variable Ð Ñ Ð Ñs s

where d kT =g kT g kTŠ ‹ Š ‹ Š ‹s s ss Ð Ñ14

i.e.

• Because has small variations, to achieve a certain level of.Ð5X Ñ=performance fewer bits are required. This implies that DPCM can achievePCM performance levels with lower bit rates.

• 6dB Law: SNR 15where 10dB 7.77dB

; œ %Þ(( ' Ð Ñ

# a in dBa

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 36 Prof. A. Manikas

A BETTER DIFFERENTIAL QUANTIZER: mse Diff. Quant.

• the largest error reduction occurs when the differential quantizer operates on

the differences between and the minimum mean square errorg kTÐ Ñs

Ð Ñ Ð Ñ Ð Ñmin-mse estimator of g kT g kT^ s s

Ð ÑN.B.: but more hardware

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 37 Prof. A. Manikas

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 38 Prof. A. Manikas

g kT = .g ~sÐ Ñs wT

whereÚÛÜ

g= g k T , g k T , ....., g k L T ~ ~ ~ ~

= w , w , ....., w

’ “Š ‹ Š ‹ Š ‹c d

Ð Ñ Ð Ñ Ð Ñ " # s s sT

Tw " # P

rule:choose to minimize for the Transmitter

choose to minimize

ÚÝÝÛÝÝÜœŠœŠ

w

w

g kT g kT ....

d kT +g kT ....

X

X

Ð Ñ Ð Ñ

Ð Ñ Ð Ñ

s s

q s s

s

s

‹‹

#

#

for the Receiver

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 39 Prof. A. Manikas

DIFFERENTIAL QUANTIZERS: Examples

The power of can be found as follows:d kT s

5 X X X

5 5

d s s

g g

# # # #

# #

œ "š › š › š Š ‹›ðóóóñóóóò ðóóóóóóóñóóóóóóóòd = g kT + g k T

Ð Ñ Ð Ñ

. g kT . g k T

.R T

# "

#

ðóóóóóóóóóóóóóñóóóóóóóóóóóóóòš Š ‹ Š ‹›X s s

gg s

Ð Ñ

Ð Ñ

Ê # # Ê # " 5 5 5 5d dg ggg sR T# # # # = . .R T = . . Ð Ñ Ð ÑŠ ‹gg s

g

Ð Ñ5# 16

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 40 Prof. A. Manikas

e.g.

disadvantages: unrecoverable degradation is introduced by the quantisationprocess. (Designers task is to keep this to a subjective acce table level):

• :Remember

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 41 Prof. A. Manikas

1) =R 05g gg# Ð Ñ

2) is known as the autocorrelation function = normalizedRgg

g

Ð Ñ75#

3) DPCM with the same No of bits/sample generally gives better results Ä than PCM with the same number of bits.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 42 Prof. A. Manikas

• Example of mse DPCM

assume a 4-level quantizer : input +input +input 1

5 input

I/P O/P & Ÿ Ÿ #&& (! Ÿ Ÿ % "

% Ÿ Ÿ " #& Ÿ Ÿ & (

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 43 Prof. A. Manikas

INPUT step from 0V to 26V

i/p prediction error quant. error o/pA E =D B =A -E C D =C +En

26 0 2 +7 726 7 1 +7 1426 14 1 +7 2126 21 +7 2826 2

n n n-1 n n n n n n

'*#&

) # "( " "' ! "

#' #(

2726 2 2626 2 2726 26

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 44 Prof. A. Manikas

INPUT step from 0V to 25V

i/p prediction error quant. error o/pA E =D B =A -E C D =C +En

25 0 25 +7 725 7 18 +7 1425 14 11 +7 2125 21 4 +1 2225 22 3 +1

n n n-1 n n n n n n

2325 23 2 +1 2425 24 1 +1 2525 25 0 26

5 5# #

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 45 Prof. A. Manikas

4. NOISE EFFECTS in a binary PCMì It can be proved that the Signal-to-Noise Ratio at the output of a binary

Pulse Code Modulation (PCM) system, which employs a BCDencoder/decoder and operates in the presence of noise, is given by thefollowing expression

SNRout= XX X

e fe f e fgn n

!#

! !# #

Ð>ÑÐ>Ñ Ð>Ñq

= 21+4. .2

#

#

#

#pe

where (type of digital modulator) EUEp = p = .e ef Tœ È ŸÐ" Ñ3

e.g. if the digital modulator is a PSK-mod. then EUEp = .e T È Ÿ#

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 46 Prof. A. Manikas

4.1. THRESHOLD EFFECTS in a binary PCM

ì We have seen that: SNRout=2

1+4. .2#

#

#

#pe

ì Let us examine the following two cases: SNR =high and SNR =low38 38

i) =HIGH ii) =LOWSNR SNRin in

SNR SNRin e in e=high p =small =low p =largeÊ Ê

Ê " % # ¶ ".p . e##

Ê ¶ # Ê " % # ¶ % #SNRout e e# # ## # # .p . .p .

Ê ¶ Ê ¶SNR dB SNRout out .p6 # "% e

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 47 Prof. A. Manikas

ì :THRESHOLD POINT- definition

Threshold point is arbitrarily definedas the SNR at which the SNR (i.e. ) in out p

21+4. .2

#

#

#

#efalls 1dB

below the maximum SNR (i.e. 1dB below the value 2 ).out##

ì By using the above definition it can be shown (...for you ...) that thethreshold point occurs when

p =e ."

"' ###

where is the number of bits per level.#

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 48 Prof. A. Manikas

SNRout

SNRin

1dB γ=8γ=7

γ=6

γ=5

6dB

6dB

6dB

(dB)

(dB)SNRin,threshold

for γ=8

4.2. COMMENTS on THRESHOLD EFFECTSì Å in PCM will result in a sudden in .The onset of threshold the output noise powerì of Psignal= SNR = SNRÅ Ê Å Ê38 out reaches 6 dB and becomes independent# P=318+6

.. . above threshold: SNRincreasing signal power no further improvement inÊ outì The limiting value of depends only on the number of bits perSNRout #

quantization levels

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 49 Prof. A. Manikas

5. DIFFERENTIAL PCM (DPCM)

• DPCM = PCM which employs a differential quantizer

i.e. DPCM reduces the correlation that often exists between successive PCMsamples

• The CCITT standards 32 DPCM The CCITT standards 64 DPCMkbits kbitssec sec

speech signal - kHz audio signal - kHzJ œ $Þ# J œ (1 1

J œ ) J œ "'

U œ "' U œ "'

= =ksamples ksamples

sec secbits bitslevel levellevels i.e. =4 levels i.e. =4ˆ ‰ ˆ ‰# #

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 50 Prof. A. Manikas

Problems of DPCM:

1. slope overload noise:occurs when outer quantization level is too small for large inputtransitions and has to be used repeatedly

2. "Oscilation" or granular noise:occurs when the smallest -level is not zero. Then, for constant input,Uthe coder output oscillates with amplitude equal to the smallest -Ulevel.

3. "Edge Busyness" noise:occurs when repetitive edge waveform is contaminated by noise whichcauses it to be coded by different sequences of -levels.U

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 51 Prof. A. Manikas

6. INTRODUCTION to TELEPHONE NETWORKsubscriber-A: 1784-382384 subscriber-B:20759 46266

PSTNTwistedcoperpair

Twistedcoperpair

Junc tion box (network Termination)

Junc tion box (network Termination)

Note that, as calls are routed through the PSTN, they will berouted ( ) through a multiplexed hierarchy of switchingcenters

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 52 Prof. A. Manikas

PSTNEnd Office - Class 5

Toll Center - Class 4

Primary Center - Class 3

Sectional Center - Class 2

Regional Center - Class 1

… …

…Local Loop Local Loop

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 53 Prof. A. Manikas

ì 1960 British Post Office (BPO) (currently BT) had establisheda with objective the system to be available24-ch PCM systemin 1968. Some of this work become the basis to the formationof a number of CCITT recommendations.

ì In Europe, the original , which were24-ch PCM systemsdesigned mainly for up to 32Km transmission routes, havebeen replaced by .30-ch PCM systems

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 54 Prof. A. Manikas

ì There are CCITT recommendations for PCM.two differentThe main differences between these two recommendations areshown in the following table:

PCM CCITT RECOMMENDATIONS1st Recommentation 2nd Recommentation

Package SizeEncoding Law

=255 (but

24-channels -law

30-channels. E-law. they use =100), =

=7 ; =8 =8 FA-signal is FA-word is placed

.

# # #

E )(Þ'5 bits bits bits6 samples samples samples

Frame-Alignm

distributed ent

Signalling

amongst several frames into a separate slot ( )Signalling information is Signalling information conveyed

TS0

within each for all 30-channels encoded and conveyed in a separate 8-bit TS ( )

Strategies speech-time-slotTS-16

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 55 Prof. A. Manikas

That is,1st CCITT rec. (24-channels PCM)

TS1 TS2 TS24

8 bits

TS3 TS41

bit

T Fs s=1/ =125 secμ

FrameAlignment1/6 bits Signaling Information

1 2 3 4 248 bits 8 bits 8 bits 8 bits

= 193 bitsX=

2nd CCITT rec. (30-channels PCM)

Frame Alignment Signaling Information[4bits k user + 4bits (k+15) user]th th

TS0 TS1 TS31

8 bits

TS1 TS3

T Fs s=1/ =125 secμ

1 2 3 308 bits 8 bits 8 bits 8 bits

TS16TS15 TS17

15 168 bits

= 256 bitsX=

1 k 15Ÿ Ÿ

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 56 Prof. A. Manikas

ì Note:

ˆ A-law=better than -law (cheaper to produce and easy equipment.maintenance, smaller quantization error in particular within themost significant part of the dynamic range).

ˆ in 24-ch PCM the signalling information is conveyed within eachspeech time-slot (technique known as bit stealing). Result: a slightreduction in speech-coding performance.

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 57 Prof. A. Manikas

Single-Channel Path of 2nd CCITT rec. (30-channels PCM)

Message signal

bandwidth=4kHzFg

SamplingFrequency

=8kHzFs

Uniformquantizer

=2Q 8

PAMHIGHWAY

i.e. =64kbits/s rb

HDB3Line Codee

8bits

PCM HIGHWAY

A-lawA=87.6

γ=8Gray Code

bitslevel

Bit rate=γ.Fs

3rduser(say)

Frame Alignment Signaling Information

TS0 TS1 TS31

8 bits

TS1 TS3

T Fs s=1/ =125 secμ

1 2 3 308 bits 8 bits 8 bits 8 bits

TS16TS15 TS17

15 168 bits

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 58 Prof. A. Manikas

Implementation of 2nd PCM CCITT RECOMM. (First Level Mltplx )

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 59 Prof. A. Manikas

ì Based on the 24-channels amd 30-channels PCM CCITT recommendations(primary multiplex groups) the core telephone network evolved from usingFrequency Division Multiplex (FDM) technology to digital transmission andswitching

ì These two PCM CCITT recommendations have led to two PDH( digital hierarchies) CCITT reccommendations forPlesiochronousassembling the TDM telephony data streams from different calls.

ì Plesiochronous means:" because bits are stuffed into the frames asalmost synchronouspadding and the calls location varies slightly - jitters - from frame toframe"

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 60 Prof. A. Manikas

PDH Hierarchy

Hierarchical American European

0 64 kbits/s 64 kbits/s

1 1,544 kbits/s

Level DS-

DS-0

DS-1

B CEPT-

CEPT-0

CE

B

PT-1

CEPT-2

CEPT-3

2,048 kbits/s

2 6,312 kbits/s 8,448 kbits/s

3 44,736 kbits/s 34,368 kbits/s

4

DS-2

DS-3

DS-4 274,176 kbits/s 139,264 kbits/s

5 565,148 kbits/s

CEPT-4

CEPT-5

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 61 Prof. A. Manikas

ì The 24-channel PDH TDM CCITT recommendation (DS-x)

ì The 30-channel PDH TDM CCITT recommendations (CEPT-x)

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 62 Prof. A. Manikas

Main disadvantage of PDH Networks

ì PDH multiplexing was designed for point-to-point communications andchannels cannot be added to, or extracted from, a higher multiplexing leveldemultiplexing down and then multiplexing up again, throught the entirePDH

ì For instance, to isolate a particular call from DS4, say, it must bedemultiplexed to DS1.

ì i.e. this is and needs very expensive equipmenta very complex procedureat every exchange to demultiplex and multiplex high speed lines

ì American & European Telephone Systems (thereforeare incompatiblevery expensive equipment required to translate one format to the other fortransatlantic traffic )

ì Solution: SONET/SDH Signal Hierarchy

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 63 Prof. A. Manikas

SDH (Synchronous Digital Hierarchy)

ì The tranditional are based on the DS (USA) and CEPTPDH standards(Europe) PCM systems (24-channels and 30-channels PCM CCITTrecommendation)

ì PDH hierarchy is synchronous (extra bits are inserted into thealmostdigital signal stream to bring them to a common rate.

ì In 1988 was adopted by ITU andSDH (Synchronous Digital Hierarchy)ETSI (European Telecommunications Standards Instritute) based onSONET (synchronous optical Networks)

ì SDH signals have a common external timing i.e. SDH is synchronous

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 64 Prof. A. Manikas

ì The used in Europe areSDH standards

which provides Mbits/secSTM-1 155

which provides Mbits/secSTM-2 310

which provides Mbits/secSTM-3 465

which provides Mbits/secSTM-4 620

etc (increments of Mbits/sec )155

ì The most important main standards are , and .STM-1 STM-4 STM-16These are commercially available

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 65 Prof. A. Manikas

SONET/SDH Hierarchy

Hierarchical American European Level SONET SDH

0 3

1 12

2 48

STS- ST -

ST -3 ST -1

ST -12 ST -4

ST -48

B BM

M CEPT-

M CEPT-4

S DS-3

S DS-3

S

œ ‚ œ "‚

œ ‚ œ %‚

œ ‚

%

DS-3 ST -16M CEPT-œ "'‚ %

Key Advantagesì it is channels to meet customer requirementssimple to add and dropì more bandwidth is available for network managementì equipment is smaller and cheaperì network flexibilityì integrate and manage on a single fiber.various types of traffic

Principles of Communication Theory & Systems Compact Lecture Notes

PCM & PSTN 66 Prof. A. Manikas

PDH NetsSDH Nets

Mobile NetsATM Nets

IP NetsInteligent Networks

etc.Network Gateways

POTSxDSL2G3G

B-ISDNbluetoothethernet

GUIetc.

AccessNetworks

AccessNetworks

CORENetworks

POTSxDSL2G3G

B-ISDNbluetoothethernet

GUIetc.

AccessNetwork

No.1

CORENetwork

No.2

CORENetwork

No.1

CORENetwork

No.3

AccessNetwork

No.3

Gateway Interface


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