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
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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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DM System: Transmitter and Receiver.
The modulator consists of a comparator, a quantizer, and an accumulator. The output of the accumulator is
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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
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3
1
=
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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.
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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
−+=
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)/()12(41
)2(3
pn
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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