Coding technology Coding technology

Coding technology Coding technology

Lecturer:

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

• Course website:

www.hit.bme.hu/~ceffer/kodtech

Course information Course information

REQUIREMENTS:

•One major tests (with recap 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 !

•Exam (same type of problems as in midterm test)

LECTURES:

•Thursday 14.15-16.00 (R516)

•Friday 10.15-12.00 (QBF11)

Fail (1) Pass (2) Satisfactory (3) Good (4) Excellent (5) 0-39 points 40-53 points 54-67 points 68-81 points 82-100 points

GRADING POLICY:

Suggested literature and references 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

Coding technologies = e-world (systems and services)

“Network” and “data” ! Aim of coding technologies: expanding the boundaries of networks +

mining “value” out of ” data (Cloud, IoT, WSN, Big Data)

Google letöltédownloads Integrated financial services ,

algo-trading Monitoring and surveillance

Body sensors

On-line social media Energy cons.

Autonomous vehicles

Main components of ICT

Coding technologies: data communication and data compression algorithms

Networking (IoT, WSN ..etc.) Storage: cloud computing Porcessing: Big Data

23-03-10 6

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

communication systems!

23-03-10 7

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

23-03-10 TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 9

Frequency allocation

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

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 mobile technologies 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)

Basic principles

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

CHANNEL

Coding Decoding

Source coding

0000 0001 0010 00110100 0101 1111

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

# of bits appr. One-fourth symbols codewo

rds

a1 01

a2 10111

a3 111

a4 110

aN 01110

Optimal codetable ?

Channel coding

Unreliable channel

010010110 0110111010

Unreliable channel

00000

5x repeat

0 Majority 0

detector

01010

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

of dataspeed?

Cryptography

Public channel

Cypher Decypher

message message

key attacker key

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 Summary

Primer info (voice,

image..etc.) Channel

Retrieved

Alg. info

Corrupt recepetion

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.

Corresponding algorithms:

Coding technology

BSC as an additive channel model

Binary Symmetric Channel

 ^0,1

yk  y^ˆk  ^0,1

Error bit

y

e

ˆ

y   y e

ˆ 0 0 0 0 1 1 1 0 1 1 1 0

k k k

y e y

Extension to vectors

error vector

y

e

  ^{ }

^{ }

^{ }

 

 

 

,ˆ ,ˆ

ˆ ˆ 1 1

1 1

1

n d n w

d w

b b b b

w

n w n

b

b b

b

P P P P P P

P P P

P 

 

      

 

      

y y e

y y e

e

e

y y e y y

Block error probability

How to achieve reliable communication over an unreliable channel

5x BSC Majority dec.

0 00000 01010

errors

1

b 0.01 P 

BSC’

BSC’

 

5 5 4 2

3

' 5 ⁱ 1 ⁱ 10 10

b b b b

i

P P P P

i

  



      



Problem: for the sake of reliable communication we have to decrease the

data speed

Reliable communication by repeaters

Better QoS

Loss in data speed

THANK YOU FOR YOR

ATTENTION !