1. EC6501 DIGITAL COMMUNICATION

2. OBJECTIVES:  To know the principles of sampling & quantization
 To study the various waveform coding schemes
 To learn the various baseband transmission schemes
 To understand the various Band pass signaling schemes
 To know the fundamentals of channel coding

3. SYLLABUS
UNIT I SAMPLING & QUANTIZATION 9 Low pass sampling – Aliasing- Signal Reconstruction-Quantization - Uniform & non-uniform quantization - quantization noise - Logarithmic Companding of speech signal- PCM - TDM 56 UNIT II WAVEFORM CODING 9 Prediction filtering and DPCM - Delta Modulation - ADPCM & ADM principles-Linear Predictive Coding UNIT III BASEBAND TRANSMISSION 9 Properties of Line codes- Power Spectral Density of Unipolar / Polar RZ & NRZ – Bipolar NRZ - Manchester- ISI – Nyquist criterion for distortionless transmission – Pulse shaping – Correlative coding - Mary schemes – Eye pattern - Equalization UNIT IV DIGITAL MODULATION SCHEME 9 Geometric Representation of signals - Generation, detection, PSD & BER of Coherent BPSK, BFSK & QPSK - QAM - Carrier Synchronization - structure of Non-coherent Receivers - Principle of DPSK. UNIT V ERROR CONTROL CODING 9 Channel coding theorem - Linear Block codes - Hamming codes - Cyclic codes - Convolutional codes - Vitterbi Decoder TOTAL: 45 PERIODS

4. OUTCOMES Upon completion of the course, students will be able to
 Design PCM systems
 Design and implement base band transmission schemes
 Design and implement band pass signaling schemes
 Analyze the spectral characteristics of band pass signaling schemes and their noise performance
 Design error control coding schemes

5. EC6501 DIGITAL COMMUNICATION
UNIT - 1

6. INTRODUCTION

10. UNIT I SAMPLING & QUANTIZATION (9)
Low pass sampling
Aliasing
Signal Reconstruction
Quantization
Uniform & non-uniform quantization
Quantization Noise
Logarithmic Companding of speech signal
PCM
TDM

12. Digital communication system
Input
Signal
Analog/
Digital
Low
Pass
Filter
Sampler
Quantizer
Source
Encoder
Channel
Encoder
Multiplexer
Carrier
Modulator
Pulse
Shaping
Filters
Line
Encoder
To Channel
De-
Modulator
Receiver
Filter
Detector
From Channel
Carrier Ref.
Signal
at the
user end
Digital-to-Analog
Converter
Channel
Decoder
De-
Multiplexer

13. Key Questions
How can a continuous wave form be converted into discrete samples?
How can discrete samples be converted back into a continuous form?

14. Low Pass Sampling Sampling (in time) is
Measure amplitude at regular intervals
How many times should we sample?

15. Nyquist Theorem
For lossless digitization, the sampling rate should be at least twice the maximum frequency of the signal to be sampled.
In mathematical terms:
fs > 2*fm
where fs is sampling frequency and fm is the maximum frequency in the signal

16. Limited Sampling
But what if one cannot sample fast enough?

17. Limited Sampling
Reduce signal frequency to half of maximum sampling frequency
low-pass filter removes higher-frequencies
(e.g.) If max sampling frequency is 22kHz, the it is a must to low-pass filter a signal down to 11kHz

24. Aliasing effect
LP filter
Nyquist rate
aliasing

25. Three different sampling methods
Practical Sampling Methods are Natural Sampling and Flat-top Sampling

26. Natural Sampling

28. Pulse-Amplitude Modulation
Pulse-Amplitude Modulation (PAM)
The amplitude of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal.
Two operations involved in the generation of the PAM signal
Instantaneous sampling of the message signal m(t) every Ts seconds,
Lengthening the duration of each sample, so that it occupies some finite value T.
Fig. 5

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Fig.5

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Fig.6

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Fig.7

32. The advantages offered by digital pulse modulation
Performance
Digital pulse modulation permits the use of regenerative repeaters, when placed along the transmission path at short enough distances, can practically eliminate the degrading effects of channel noise and signal distortion.
Ruggedness
A digital communication system can be designed to withstand the effects of channel noise and signal distortion
Reliability
Can be made highly reliable by exploiting powerful error-control coding techniques.
Security
Can be made highly secure by exploiting powerful encryption algorithms
Efficiency
Inherently more efficient than analog communication system in the tradeoff between transmission bandwidth and signal-to-noise ratio
System integration
To integrate digitized analog signals with digital computer data

33. Quantization Process Amplitude quantization
The process of transforming the sample amplitude m(nTs) of a baseband signal m(t) at time t=nTs into a discrete amplitude v(nTs) taken from a finite set of possible levels.
Representation level (or Reconstruction level)
The amplitudes vk , k=1,2,3,……,L
Quantum (or step-size)
The spacing between two adjacent representation levels
Fig. 9
Fig. 10

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Fig.9

35. Two types of quantization are Mid-tread Mid-rise
Back
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Fig.10
Two types of quantization are
Mid-tread
Mid-rise

36. Linear Quantization
Applicable when the signal is in a finite range (fmin, fmax)
The entire data range is divided into L equal intervals of length Q (known as quantization interval or quantization step-size)
Q=(fmax-fmin)/L Interval i is mapped to the middle value of this interval
We store/send only the index of quantized value min

37. Signal Range is Symmetric

38. Quantization Noise

39. Non-Uniform Quantization
Many signals such as speech have a nonuniform distribution.
The amplitude is more likely to be close to zero than to be at higher levels.
Nonuniform quantizers have unequally spaced levels
The spacing can be chosen to optimize the SNR for a particular type of signal.
Output sample XQ 6 4 2
Example: Nonuniform 3 bit quantizer -8 -6 -4 -2 2 4 6 8
Input sample X -2 -4 -6

40. Non-Linear Quantization
The quantizing intervals are not of equal size
Small quantizing intervals are allocated to small signal values (samples) and large quantization intervals to large samples so that the signal-to-quantization distortion ratio is nearly independent of the signal level
S/N ratios for weak signals are much better but are slightly less for the stronger signals
“Companding” is used to quantize signals

41. Function representation

42. Uniform and Non-uniform Quantization

43. Companding Formed from the words compressing and expanding.
A PCM compression technique where analogue signal values are rounded on a non-linear scale.
The data is compressed before sent and then expanded at the receiving end using the same non-linear scale.
Companding reduces the noise and crosstalk levels at the receiver.

44. u-LAW and A-LAW definitions
A-law and u-law are companding schemes used in telephone networks to get more dynamics to the 8 bit samples that is available with linear coding.
Typically bit samples (linear scale) sampled at 8 kHz sample are companded to 8 bit (logarithmic scale) for transmission over 64 kbit/s data channel.
In the receiving end the data is then converted back to linear scale ( bit) and played back. converted back

45. Compressor Fig. 5.11 A particular form of compression law : μ-law
μ-law is neither strictly linear nor strictly logarithmic
A-law :
Fig. 5.11

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Fig.11

47. Example: m-law Companding
x[n]=speech /song/
y[n]=C(x[n])
Companded Signal
Close View of the Signal
Segment of x[n]
Segment of y[n]
Companded Signal

48. A-law and m-law Companding
These two are standard companding methods.
u-Law is used in North America and Japan
A-Law is used elsewhere to compress digital telephone signals

49. Quantization - why do we need such classification ?! - (3)
Comparison – Uniform Vs. Non-Uniform Usage
Speech signals doesn’t require high quantization resolution for
high amplitudes (50% Vs. 15%).
wasteful to use uniform quantizer ?
The goal is decrease the SQNR, more levels for low amplitudes, less levels for high ones.
Maybe use a Non-uniform quantizer ?
A good Idea is to use a non-uniform quantizer . A non-uniform quantizer can provide fine
quantization levels for weak signals ( 50% ) and coarse levels for strong signals (15%) .
The goal is decrease the SQNR . And the SQNR is proportional to the number of levels,
specially at the weak signal part.
Technical Presentation  Page 49

50. Concepts Quantization More About Non-Uniform Quantizers (Companding)
Uniform quantizer = use more levels when you need it.
The human ear follows a logarithmic process in which high amplitude sound doesn’t
require the same resolution as low amplitude sounds.
One way to achieve non-uniform quantization is to use what is called as “Companding”
Companding = “Compression + Expanding”
Uniform
Quantization
Compressor
Function
Expander
Function
Example from the lecture of Prof. S.N.Merchant.
Tasks:
Put the Example for Comapding
Explain Mu-Law and A-Law
Understanding from where does the 13 kBit Come From.
Explain
It should be noted that, A-Law and M-Law are used to compress the 13 or 14 bit signed linear PCM samples to logarithmic 8 bit samples
(-1)
Technical Presentation  Page 50

51. Pulse-Code Modulation
PCM (Pulse-Code Modulation)
A message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude
The basic operation
Transmitter : sampling, quantization, encoding
Receiver : regeneration, decoding, reconstruction
Operation in the Transmitter
Sampling
The incoming message signal is sampled with a train of rectangular pulses
The reduction of the continuously varying message signal to a limited number of discrete values per second
Nonuniform Quantization
The step size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end-step of the quantizer can take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently.

52. Back
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Fig.11

53. Encoding
To translate the discrete set of sample vales to a more appropriate form of signal
A binary code
The maximum advantage over the effects of noise in a transmission medium is obtained by using a binary code, because a binary symbol withstands a relatively high level of noise.
The binary code is easy to generate and regenerate
Fig. 11
Table. 2

54. Regeneration Along the Transmission Path
The ability to control the effects of distortion and noise produced by transmitting a PCM signal over a channel
Equalizer
Shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the transmission
Timing circuitry
Provides a periodic pulse train, derived from the received pulses
Renewed sampling of the equalized pulses
Decision-making device
The sample so extracted is compared o a predetermined threshold
ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal
The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal
If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion.
Fig. 13

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Fig.13

56. Operations in the Receivers
Decoding and expanding
Decoding : regenerating a pulse whose amplitude is the linear sum of all the pulses in the code word
Expander : a subsystem in the receiver with a characteristic complementary to the compressor
The combination of a compressor and an expander is a compander
Reconstruction
Recover the message signal : passing the expander output through a low-pass reconstruction filter

57. Categories of multiplexing

58. Time Division Multiplexing (TDM)
TDM is a technique used for transmitting several message signals over a single communication channel by dividing the time frame into slots, one slot for each message signal

59. Time Division Multiplexing
Entire spectrum is allocated for a channel (user) for a limited time.
The user must not transmit until its
next turn.
Used in 2nd generation
Advantages:
Only one carrier in the medium at any given time
High throughput even for many users
Common TX component design, only one power amplifier
Flexible allocation of resources (multiple time slots). f t c k2 k3 k4 k5 k6 k1
Frequency
Time

60. Time Division Multiplexing
Disadvantages
Synchronization
Requires terminal to support a much higher data rate than the user information rate therefore possible problems with intersymbol-interference.
Application: GSM
GSM handsets transmit data at a rate of 270 kbit/s in a 200 kHz channel using GMSK modulation.
Each frequency channel is assigned 8 users, each having a basic data rate of around 13 kbit/s

61. Time Division Multiplexing
At the Transmitter
Simultaneous transmission of several signals on a time-sharing basis.
Each signal occupies its own distinct time slot, using all frequencies, for the duration of the transmission.
Slots may be permanently assigned on demand.
At the Receiver
Decommutator (sampler) has to be synchronized with the incoming waveform  Frame Synchronization
Low pass filter
ISI – poor channel filtering
Feedthrough of one channel's signal into another channel -- Crosstalk
Applications of TDM: Digital Telephony, Data communications, Satellite Access, Cellular radio.

62. Time Division Multiplexing
Conceptual diagram of multiplexing-demultiplexing.
PAM TDM System

63. TDM-PAM: Transmitter

64. TDM-PAM : Receiver

65. Samples of Signal -1
g1(t)
time Ts
2Ts

66. Samples of signal - 2 Ts
g2(t)

67. Multiplexing of TWO signalsTs
2Ts

68. TDM-PAM for 4 signals. 1 2 3 4
Time

69. Problem
Two low-pass signals of equal bandwidth are sampled and time division multiplexed using PAM. The TDM signal is passed through a Low-pass filter & then transmitted over a channel with a bandwidth of 10KHz.
Continued….

70. Problem (continued…) What is maximum Sampling rate for each Channel?
What is the maximum frequency content allowable for each signal?

71. Problem: Solution Channel Bandwidth = 10 KHz.
Number of samples that can be transmitted through the channel = 20K
Maximum Sampling rate for each channel = 10K Samples/sec.
Maximum Frequency for each Signal = 5KHz

72. End of Unit-1