Coding technology Lecturer: Prof. Dr. János LEVENDOVSZKY (levendov@hit.bme.hu) Course website: www.hit.bme.hu/~ceffer/kodtech

Course information REQUIREMENTS: LECTURES: Thursday 14.15-16.00 Friday 10.15-12.00 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) GRADING POLICY:

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) Google letöltédownloads Integrated financial services , algo-trading Monitoring and surveillance Body sensors On-line social media Energy cons. Autonomous vehicles “Network” and “data” ! Aim of coding technologies: expanding the boundaries of networks + mining “value” out of ” data (Cloud, IoT, WSN, Big Data)

Main components of ICT Networking (IoT, WSN ..etc.) Storage: cloud computing Porcessing: Big Data Coding technologies: data communication and data compression algorithms

Course objective: algorithmic skills and knowledge (coding procedures) for increasing the performance of communication systems! 2018.04.16. 6 6

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 !!! 2018.04.16. 7

Replacing resources by algorithms !!! General objective Replacing resources by algorithms !!! Modern communication technologies = smart algorithms and protocols to overcome the limits of the resources 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

Frequency allocation http://en.wikipedia.org/wiki/File:United_States_Frequency_Allocations_Chart_2003_-_The_Radio_Spectrum.jpg 2018.04.16. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 9 TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 9

QoS = f (resources) ??? RESOURCES: e.g. bandwidth, transmission power 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 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 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: 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

Limited resources (transmission power, bandwidth …etc.) Basic principles 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 CHANNEL Coding Decoding ALGORITHMS ??

# of bits appr. One-fourth Source coding 0000 0001 0010 0011 0100 0101 1111 symbols codewords a1 01 a2 10111 a3 111 a4 110 aN 01110 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 Unreliable channel 5x repeat 010010110 0110111010 Unreliable channel 00000 5x repeat Majority detector 01010 What is the optimal code guaranteeing a predefined relaibility with minimum loss of dataspeed?

Cryptography Public channel attacker key key message Public channel Decypher message Cypher 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 ?

Primer info (voice, image..etc.) Summary Corrupt recepetion Retrieved info Alg. Primer info (voice, image..etc.) Alg. Channel Challenges: What is the ultimately compressed representation of information ? What is the data rate and by what algorithms over which can communicate reliably over unreliable channels ? How can we communicate securely over public systems? Corresponding algorithms: Coding technology

BSC as an additive channel model Binary Symmetric Channel Error bit

Extension to vectors error vector

Block error probability

How to achieve reliable communication over an unreliable channel BSC’ errors 1 00000 01010 5x BSC Majority dec. BSC’ Problem: for the sake of reliable communication we have to decrease the data speed

Reliable communication by repeaters Better QoS Loss in data speed

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