ECE 4371, Fall, 2013 · 2014-12-18 · Pulse Code Modulation (PCM) Pulse code modulation (PCM) is produced by analog-to-digital conversion process. Quantized PAM As in the case of

ECE 4371, Fall, 2013

Introduction to Telecommunication Engineering/Telecommunication Laboratory

Zhu Han

Department of Electrical and Computer Engineering

Class 9

Sep. 25th, 2013

OutlineOutline

� Review of quantization

– 6dB rule

– Two optimal rules

� PCM, DPCM, ADPCM

� Delta modulation

� Error in PCM

� T carrier system (cable and fiber communication)

Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)

� Pulse code modulation (PCM) is produced by analog-to-digital conversion

process. Quantized PAM

� As in the case of other pulse modulation techniques, the rate at which

samples are taken and encoded must conform to the Nyquist sampling rate.

� The sampling rate must be greater than, twice the highest frequency in the

analog signal,

fs > 2fA(max)

� Telegraph time-division multiplex (TDM) was conveyed as early as 1853, by

the American inventor M.B. Farmer. The electrical engineer W.M. Miner, in

1903.

� PCM was invented by the British engineer Alec Reeves in 1937 in France.

� It was not until about the middle of 1943 that the Bell Labs people became

aware of the use of PCM binary coding as already proposed by Alec Reeves.

Figure Figure The basic elements of a PCM system.The basic elements of a PCM system.

Pulse Code Modulation

Encoding

Advantages of PCM

1. Robustness to noise and interference

2. Efficient regeneration

3. Efficient SNR and bandwidth trade-off

4. Uniform format

5. Ease add and drop

6. Secure

DS0: a basic digital signaling rate of 64 kbit/s. To carry a typical

phone call, the audio sound is digitized at an 8 kHz sample rate

using 8-bit pulse-code modulation. 4K baseband, 8*6+1.8 dB

Virtues, Limitations and Modifications of PCM

� Encode information in terms of signal transition; a transition is used to designate Symbol 0

Regeneration (reamplification, retiming, reshaping )

3dB performance loss, easier decoder

Differential Encoding

1 1 1 1

Consider a finite-duration impulse response (FIR)

discrete-time filter which consists of three blocks :

1. Set of p ( p: prediction order) unit-delay elements (z-1)

2. Set of multipliers with coefficients w1,w2,…wp

3. Set of adders ( ∑ )

Linear Prediction Coding (LPC)

Block diagram illustrating the linear adaptive prediction process.

Reduce the sampling rate

Differential Pulse-Code Modulation (DPCM)

Usually PCM has the sampling rate higher than the Nyquist rate.

The encode signal contains redundant information. DPCM can efficiently

remove this redundancy. 32 Kbps for PCM Quality

[ ] [ ]

) (minimize G maximize filter to prediction aDesign

G Gain, Processing

)SNR(

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))(((SNR)

and 0)]][[( of variancesare and where

(SNR)

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2

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2

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2

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2

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o

22

2

2

o

o

Ep

E

M

p

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EQ

E

Qp

Q

E

E

M

QM

Q

M

G

nqnmEnm

σ

σσ

σσ

σ

σσ

σσ

σσ

σσ

=

=

=

=

=

=

Processing Gain

Need for coding speech at low bit rates , we have two aims in mind:

1. Remove redundancies from the speech signal as far as possible.

2. Assign the available bits in a perceptually efficient manner.

Adaptive quantization with backward estimation (AQB).

Adaptive Differential Pulse-Code Modulation (ADPCM)

ADPCM

Adaptive prediction with backward estimation (APB).

8-16 kbps with the same quality of PCM

Coded Excited Linear Prediction (CELP)Coded Excited Linear Prediction (CELP)

� Currently the most widely used speech coding algorithm

� Code books

� Vector Quantization

� <8kbps

� Compared to CD

44.1 k sampling

16 bits quantization

705.6 kbps

100 times difference

Delta Modulation (DM)

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[ ] [ ] [ ][ ] [ ][ ] [ ] [ ]

[ ] [ ][ ] size step theis and , of version quantized the

is ,output quantizer theis where

1

) sgn(

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).( of sample a is )( and period sampling theis where

,2,1,0 , )(Let

∆

+−=

∆=

−−=

±±==

ne

nenm

nenmnm

nene

nmnmne

tmnTmT

nnTmnm

qq

qqq

q

q

ss

s K

DM System: Transmitter and Receiver.

The modulator consists of a comparator, a quantizer, and an accumulator. The output of the accumulator is

[ ] [ ]

[ ]

)sgn(

1

1

∑

∑

=

=

=

∆=

n

i

q

n

i

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ienm

Slope overload distortion and granular noise

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≥∆

−

−−−−=

−=

Slope Overload Distortion and Granular Noise

( differentiator )

The modulation which has an integrator can

relieve the draw back of delta modulation (differentiator)

Beneficial effects of using integrator:

1. Pre-emphasize the low-frequency content

2. Increase correlation between adjacent samples

(reduce the variance of the error signal at the quantizer input )

3. Simplify receiver design

Because the transmitter has an integrator , the receiver

consists simply of a low-pass filter.

(The differentiator in the conventional DM receiver is cancelled by

the integrator )

Σ−∆

Delta-Sigma modulation (sigma-delta modulation)

delta-sigma modulation system.

Two Types of ErrorsTwo Types of Errors

� Round off error

� Detection error

� Variance of sum of the independent random variables is equal to

the sum of the variances of the independent random variables.

� The final error energy is equal to the sum of error energy for two types of errors

� Round off error in PCM

2

2

3

1

=

L

mp

qσ

Mean Square Error in PCMMean Square Error in PCM

� If transmit 1101 (13), but receive 0101 (5), error is 8

� Error in different location produces different MSE

� Overall error probability

– Gray coding: if one bit occur, the error is minimized.

)2)(2( p

i

i m−=ε

)2(3

)12(4)(

2

22

1

2

1

2

n

n

epn

i

ieie

n

i

i

PmPPMSE

−=== ∑∑

==

εεε

Bit Errors in PCM Systems

Simplest case is Additive

White Gaussian Noise for

baseband PCM scheme --

see the analysis for this

case. For signal levels of

+A and -A we get

pe = Q(A/σ)

Notes

•Q(A/σ) represents the area under one tail of the normal pdf

•(A/σ)2 represents the Signal to Noise (SNR) ratio

• Our analysis has neglected the effects of transmit and receive filters - it

can be shown that the same results apply when filters with the correct

response are used.

Q Function

� For Q function:

– The remain of cdf of Gaussian

distribution

– Physical meaning

– Equation

� Matlab: erfc

– y = Q(x)

– y = 0.5*erfc(x/sqrt(2));

� Note how rapidly Q(x) decreases

as x increases - this leads to the

threshold characteristic of digital communication systems

0 1 2 3 4 5 610

-10

10-8

10-6

10-4

10-2

100

Q Function

( )γQPe=

SNR vs. SNR vs. γγγγγγγγ

� Threshold

� Saturation

– slightly better than ADC

� Exchange of SNR for bandwidth is much more efficient

than in angle modulation

� Repeaters

−+=

2

2

0

2

2

0

0

)/()12(41

)2(3

pn

n

m

m

nQN

S

γ

TimeTime--Division MultiplexingDivision Multiplexing

Figure Block diagram of TDM system.

DS1/T1/E1DS1/T1/E1

� Digital signal 1 (DS1, also known as T1) is a T-carrier signaling scheme devised by Bell Labs. DS1 is a widely used standard in telecommunications in North America and Japan to transmit voice and data between devices. E1 is used in place of T1 outside of North America and Japan. Technically, DS1 is the transmission protocol used over a physical T1 line; however, the terms "DS1" and "T1" are often used interchangeably.

� A DS1 circuit is made up of twenty-four DS0

� DS1: (8 bits/channel * 24 channels/frame + 1 framing bit) * 8000 frames/s = 1.544 Mbit/s

� A E1 is made up of 32 DS0

� The line data rate is 2.048 Mbit/s which is split into 32 time slots, each being allocated 8 bits in turn. Thus each time slot sends and receives an 8-bit sample 8000 times per second (8 x 8000 x 32 = 2,048,000). 2.048Mbit/s

Synchronization Synchronization

� Super Frame

Synchronization Synchronization

� Extended Super Frame

T Carrier SystemT Carrier System

Twisted Wire to Cable System

Fiber CommunicationFiber Communication