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TSKS01 Digital Communication
Lecture 1
Introduction, Repetition of S&S and Probability Theory
Mikael Olofsson
Department of EE (ISY)
Div. of Communication Systems
2012-08-31 TSKS01 Digital Communication - Lecture 1 2
TSKS01 Digital Communication - Formalia
Information: www.commsys.isy.liu.se/TSKS01
Lecturer & examiner: Mikael Olofsson, [email protected]
Tutorials and labs: Antonios Pitarokoilis, [email protected]
Examination: Laborations (1hp):
Two 4 hour laborations in HT2
Sign-up on the web
Written exam (5hp):
1 simple task � Demand: 1/2
2 questions (5 points each), min 3
4 problems (5 points each), min 6
Pass: 14 points
2012-08-31 TSKS01 Digital Communication - Lecture 1 3
Course Aims 1(2)
After passing the course, the student should
� be able to reliably perform standard calculations regarding digital
modulation, binary (linear) codes for error control and source coding.
(basics)
� be generally aquainted with modern communication, especially digital
communication, i.e. be able to briefly describe several communication
techniques. (questions)
� be able to describe problems that arise in communication situations,
using own words, and be able to describe, and in a relevant way,
compare methods to counteract those problems. (questions)
2012-08-31 TSKS01 Digital Communication - Lecture 1 4
Course Aims 2(2)
After passing the course, the student should
� be able to account for the connection between different concepts in
the course in a structured way using adequate terminology.
(questions)
� be able to, with some precision, analyze and compare various choices
of digital modulation methods and coding methods in terms of error
probabilities, minimum distances and related concepts.
(problems)
� be able to implement such communication systems that are treated in
the course in block form and empirically evaluate them.
(laborations)
2012-08-31 TSKS01 Digital Communication - Lecture 1
Languages in Tutorial Sessions
5
The tutorial series scheduled for Group_B is cancelled.
All teaching will be in English.
2012-08-31 TSKS01 Digital Communication - Lecture 1 6
Overview of a Communication Situation
ChannelSender
Sampling
Reconstruction
D/A-conversion
Modulation
Channel coding
Source coding
Filtering
�
LTI - non LTI
Fading
Noise
Intentional jamming
�
Source statistics
Stochastic process
Markov chains
Auto-correlation
�
Demands on quality
Cost functions
Application
Purpose
�
Sampling
Reconstruktion
A/D-conversion
Demodulation
Channel-decoding
Source decoding
Filtering
�
ReceiverSource Destination
2012-08-31 TSKS01 Digital Communication - Lecture 1 7
A One-way Telecommunication System
Channel
Source
encoder
Source
decoder
Source
Destination
Channel
encoderModulator
Channel
decoder
De-
modulator
Source
coding
Channel
coding
Packing
Unpacking
Error control
Error correction
Digital to analog
Analog to digital
Medium
Digital
modulation
2012-08-31 TSKS01 Digital Communication - Lecture 1 8
Course Contents
� Introduction and repetition (Lecture 1)
� Introduction to stochastic processes. (Lecture 2)
� Digital modulation. (Lectures 3-6)
� Codes for error control. (Lectures 7-8)
� Practical aspects (Lectures 9-11)
� Software defined radio (lab preparation). (Lecture 12)
2012-08-31 TSKS01 Digital Communication - Lecture 1 9
Repetition Signals and Systems
System���� ����
Signals: Voltages, currents, and other measurements.
Systems: Manipulate signals.
Complex exponential: ������������������������ �����
Unit step: ���� �
Unit impulse: ��:
Property:
�����
� �
����������������������������
���� ����δ����� ������∞
−∞
����� ����� δ�τ ��τ�
−∞
2012-08-31 TSKS01 Digital Communication - Lecture 1 10
Special Outputs
Energy-free
system�� ����
Impulse response:
General case:
Energy-free
system���� ����
Step response:
Energy-free
system��� ����
2012-08-31 TSKS01 Digital Communication - Lecture 1 11
Linear System
2012-08-31 TSKS01 Digital Communication - Lecture 1 12
Time-Invariant and LTI
2012-08-31 TSKS01 Digital Communication - Lecture 1 13
Convolution
2012-08-31 TSKS01 Digital Communication - Lecture 1 14
Output of LTI Systems
2012-08-31 TSKS01 Digital Communication - Lecture 1 15
The Frequency domain
2012-08-31 TSKS01 Digital Communication - Lecture 1 16
LTI Systems
2012-09-04 TSKS01 Digital Communication - Lecture 2 17
Probabilities and Distributions
Probability: ��� � ∈ �����
Joint prob.: ��� ���
Cond. Prob.: ��������� �
Prob. distr.: ����� ��������∈�����
Prob. density.: ������ ������������
Properties: �������is non-decreasing
������������for all �
��∞ �����������
����������� ������ ��������
��� ��������
�
∞
���
2012-09-04 TSKS01 Digital Communication - Lecture 2 18
Example Game based on tossing two coins:
2 heads +400
2 tails �100
1 tail, one head �200
2012-09-04 TSKS01 Digital Communication - Lecture 2 19
Expectations
2012-09-04 TSKS01 Digital Communication - Lecture 2 20
Example cont�d
2012-09-04 TSKS01 Digital Communication - Lecture 2 21
Gaussian Distributions, ����σ�
2012-08-29 TSDT14 Signal Theory - Lecture 2 22
Example of the � Function
����� � ≈ ��!��" ·��#�
2012-09-04 TSKS01 Digital Communication - Lecture 2 23
Example of the � Function cont�d
���� = ��# � � ≈ !�$%
2012-09-04 TSKS01 Digital Communication - Lecture 2 24
Other Common Distributions
Exponential distribution:
Binary distribution:
Uniform distribution:
2012-09-04 TSKS01 Digital Communication - Lecture 2 25
Two-Dimensional Stochastic Variables
2012-09-04 TSKS01 Digital Communication - Lecture 2 26
Dependencies
Definition: � & � are independent if ����(�,�) = ��(�)��(�) holds.
Theorem: Independent ⇔ ����(�,�) = ��(�) ��(�) holds.
Definition: Covariance: &�'����� �(����) �������) �����
Theorem: &�'����� �(�����) ����
Definition: � & � are uncorrelated if &�'����� ��� holds.
Theorem: Independent � uncorrelated.
Note: *+���� �&�'�����
Theorem: Uncorrelated ⇔ (�����= (���(���
⇔ *+�������= *+�������*+����
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