Coding technology Lecturer: Prof. Dr. János LEVENDOVSZKY (levendov@hit.bme.hu) Course website:...

Coding technologyCoding technology

Lecturer:

• Prof. Dr. János LEVENDOVSZKY (levendov@hit.bme.hu)

• Course website: www.hit.bme.hu/~siposr/kodtech

Course informationCourse information

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 !

LECTURES:

•Wednesday 12.15 (MS Lab)

•Thursday 14.15 (MS Lab)

Suggested literature and referencesSuggested 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

CHANNEL

noise distortion e-dropping

Limited resources (transmission power, bandwidth …etc.)

Challenge: How can we communicate reliably over an unreliable channel by using limited resoures ? CODING TECHNOLOGY

CHANNELCoding Decoding

23.04.21. 5

Course objective: algorithmic skills and knowledge (coding procedures) for increasing the performance of

communication systems!

23.04.21. 6

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 !

Solution: develop intelligent algorithms to overcome these limitations !!!

Why to enhance the performance of wireless communication systems ?

E.g. - low BER requires increased transmission power

- higher data rate requires more radio spectrum

General objective

Replacing resources by algorithms !!!

Scarce and expensive Cheap and the evolution of underlying computational technology is fast

1800/1350, 1600/1200, and 1336/1000 MIPS/MFLOPS

Multibillion dollar investment

$ 100 investment

Modern communication technologies = smart algorithms and protocols to overcome the

limits of the resources

23.04.21. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 8

Frequency allocation

http://en.wikipedia.org/wiki/File:United_States_Frequency_Allocations_Chart_2003_-_The_Radio_Spectrum.jpg

Main parameters of current wireless systems

TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 923.04.21.

Demand vs. Capacity and Spectrum Occupancy

1023.04.21. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006

RESOURCES:RESOURCES: e.g. bandwidth, transmission power

DEMANDS (QoS): DEMANDS (QoS): given Bit Error Rate, Data Speed

QoS = f (resources)

???

The question telecom

companies invest money into

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

00000001001000110100

0101

1111

0000 0001 0010 0011 0100 0101 …………0000 0000 1 1 1 1 1 …………0

# of bits appr. One-fourth

symbols codewords

a1 01

a2 10111

a3 111

a4 110

aN 01110

Optimal codetable ?

Channel coding

Unreliable channel

010010110 0110111010

Unreliable channel

000005x

repeat0

0Majority detector

01010

What is the optimal code guaranteeing a predefined relaibility with minimum loss

of dataspeed?

Cryptography

Public channelCypher Decyphermessage message

key keyattacker

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 ?

SummarySummary

Primer info (voice, image..etc.)

Channel

Retrieved info

Alg.

Corrupt recepetion

QoS: BER, data rate

Challenges: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?

Alg.

Trans. power., bandwidth

RESPURCES

Corresponding algorithms:

Coding technology

THANK YOU FOR YOR ATTENTION !