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, mikael.olofsson@liu.se

Tutorials and labs: Antonios Pitarokoilis, antonios.pitarokoilis@liu.se

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

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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)

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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.

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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

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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�

−∞

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Special Outputs

Energy-free

system�� ����

Impulse response:

General case:

Energy-free

system���� ����

Step response:

Energy-free

system��� ����

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Linear System

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Time-Invariant and LTI

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Convolution

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Output of LTI Systems

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The Frequency domain

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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 �

��∞ �����������

����������� ������ ��������

��� ��������

�

∞

���

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Example Game based on tossing two coins:

2 heads +400

2 tails �100

1 tail, one head �200

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Expectations

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Example cont�d

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Gaussian Distributions, ����σ�

2012-08-29 TSDT14 Signal Theory - Lecture 2 22

Example of the � Function

����� � ≈ ��!��" ·��#�

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Example of the � Function cont�d

���� = ��# � � ≈ !�$%

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Other Common Distributions

Exponential distribution:

Binary distribution:

Uniform distribution:

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Two-Dimensional Stochastic Variables

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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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