ECE 4371, Fall, 2015

Introduction to Telecommunication Engineering/Telecommunication Laboratory

Zhu Han

Department of Electrical and Computer Engineering

Class 9

Sep. 22nd, 2015

                                                           

                                                           

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

                                                           

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(

is ratio noiseon quantizati-to-signal theanderror sprediction theof variance theis where

)SNR(

))(((SNR)

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

(SNR)

is system DPCM theof (SNR) The

2

2

2

2

2

2

2

2

2

2

o

22

2

2

o

o

Ep

E

Mp

Q

EQ

E

Qp

Q

E

E

M

QM

Q

M

G

nqnmEnm

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)

size step theis and , of version quantized the

is ,output quantizer theis where

1

) sgn(

1 is signalerror The

).( of sample a is )( and period sampling theis where,2,1,0 , )(Let

ne

nenm

nenmnm

nene

nmnmne

tmnTmTnnTmnm

qq

qqq

q

q

ss

s

                                                           

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

iq

n

iq

ie

ienm

Slope overload distortion and granular noise

                                                           

.)( of slope local the torelative large toois size step when occurs noisegranular hand,other On the

)(max (slope)

require we, distortion overload-slope avoid Tosignalinput theof difference backward

first a isinput quantizer the,1for Except 11

have We

, by error on quantizati theDenote

tm

dttdm

T

nqnqnmnmne

nqnmnmnq

s

q

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 )

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

22

31

Lmp

q

                                                           

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( pi

i m

)2(3)12(4

)( 2

22

1

2

1

2n

nep

n

iieie

n

ii

PmPPMSE

                                                           

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/)

Notes

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

•(A/)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

QPe

                                                           

SNR vs. SNR vs.

Threshold Saturation

– slightly better than ADC Exchange of SNR for bandwidth is much more efficient

than in angle modulation Repeaters

2

2

02

2

0

0

)/()12(41

)2(3

pn

n

mm

nQNS

                                                           

Time-Division MultiplexingTime-Division 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 SystemTwisted Wire to Cable System

                                                           

Fiber CommunicationFiber Communication