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#
#Å
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