Coding technology
Lecturer:
• Prof. Dr. János LEVENDOVSZKY
([email protected])
• Course website:
www.hit.bme.hu/~siposr/kodtech
Course information
LECTURES:
• Wednesday 12.15 (MS Lab)
• Thursday 14.15 (MS Lab)
REQUIREMENTS:
• One major tests (and a correction possibility)
• Signature is secured if and only if the grade of the test
(or its recap) are higher (or equal) than 2 !
• The test is partly problem solving !
Suggested literature and references
• T.M. Cover, A.J. Thomas: Elements of Information
Theory, John Wiley, 1991. (IT)
• S. Verdu, S. Mclaughlin: Information Theory: 50 years
of discovery, IEEE, 1999 (IT)
• D. Costello: Error control codes, Wiley, 2005
• S. Golomb: Basic Concepts in Information Theory and
Coding, Kluwer, 1994. (IT + CT)
• E. Berlekamp: Algebraic Coding Theory. McGraw Hill,
1968. (CT)
• R.E. Blahut: Theory and Practice of Error Correcting
Codes. Addison Wesley, 1987. (CT)
• J.G. Proakis: Digital communications,McGraw Hill,
1996
Basic principle
noise
distortion
e-dropping
CHANNEL
Limited resources (transmission power, bandwidth …etc.)
Challenge: How can we communicate reliably over an unreliable channel by using
limited resoures ? CODING TECHNOLOGY
Coding
CHANNEL
Decoding
Course objective: algorithmic skills and knowledge (coding
procedures) for increasing the performance of
communication systems!
2017.07.28.
5
Why to enhance the performance of wireless communication
systems ?
Constraints &
limitations:
- Limited power
- Limited frequency bands
- Limited Interference
???
Requirements:
- high data speed
- QoS communication
(low BER and low delay)
- Mobility
Resources (bandwidth, power …etc.) are not available !
E.g. - low BER requires increased transmission power
- higher data rate requires more radio spectrum
Solution: develop intelligent algorithms to
overcome these limitations !!!
2017.07.28.
6
General objective
Replacing resources by algorithms !!!
Cheap and the evolution of
computational
communicationunderlying
technologies
=technology
smart
is fast
Scarce and expensive
Modern
algorithms and protocols to overcome the
limits of the resources
1800/1350, 1600/1200, and 1336/1000 MIPS/MFLOPS
Multibillion dollar
investment
$ 100 investment
Frequency allocation
http://en.wikipedia.org/wiki/File:United_States_Frequency_Allocations_Chart_2003_-_The_Radio_Spectrum.jpg
2017.07.28.
TÁMOP – 4.1.2-08/2/A/KMR-2009-0006
8
Main parameters of current wireless systems
2017.07.28.
TÁMOP – 4.1.2-08/2/A/KMR-2009-0006
9
Demand vs. Capacity and Spectrum Occupancy
2017.07.28.
TÁMOP – 4.1.2-08/2/A/KMR-2009-0006
10
RESOURCES: e.g. bandwidth, transmission power
QoS = f (resources)
???
The question
telecom
companies invest
money into
DEMANDS (QoS): given Bit Error Rate, Data Speed
Spectral efficiency – a fundamental
measure of performance
SE [bit/sec/Hz] = what is the data transmission
rate achievable over 1 Hz physical sepctrum
present GSM technology
SE ~ 0.52 bit/sec/Hz
Information theory: what are the theoretical limits of SE ?
(channel dependent 5 Bit/sec/Hz)
Coding theory: by what algorithms can one achieve these theoretical
limits ?
Theoretical endeavours inspired by
technology and algorithmic solutions
• Source coding: how far the binary
representation of information
provided by data sources can be
compressed
• Channel coding: how to achieve
reliable communication over
unreliable channels
• Data security: how to implement
secure communication over public
(multi-user) channels
• Data compression
standards: APC for voice,
JPEG, MPEG
Error correcting coding:
MAC protocols (RS
codes, BCH codes,
convolutional codes)
• Data security: Public key
standards (e.g. RSA
algorithm)
Source coding
1111
symbols codewo
rds
a1
01
a2
10111
a3
111
a4
110
aN
01110
0101
0100
0011
0010
0001
0000
Optimal codetable ?
0000 0001 0010 0011 0100 0101 …………0000
0000 1 1 1 1 1 …………0
# of bits appr. One-fourth
Channel coding
Unreliable
channel
010010110
0
5x
repeat
00000
Unreliable
channel
0110111010
01010
Majority
detector
What is the optimal code guaranteeing a
predefined relaibility with minimum loss
of dataspeed?
0
Cryptography
key
message
Cypher
attacker
Public channel
key
Decypher
message
How can one construct small algorithmic complexity
cryptography algorithms which present high algorithmic
complexity for the attacker, in order to yield a given level of data
security ?
Summary
QoS: BER, data rate
Corrupt recepetion
Primer info (voice,
image..etc.)
Alg.
Channel
Alg.
Retrieved
info
Trans. power., bandwidth
RESPURCES
Challenges:
1.
What is the ultimately compressed representation of
information ?
2.
What is the data rate and by what algorithms over which
can communicate reliably over unreliable channels ?
3.
How can we communicate securely over public systems?
Corresponding
algorithms:
Coding technology
THANK YOU FOR YOR
ATTENTION !