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

2. Course 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)

3. 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

4. Basic principle CHANNEL noisedistortione-dropping Limited resources (transmission power, bandwidth …etc.) Challenge: How can we communicate reliably over an unreliable channel by using limited resoures ? CODING TECHNOLOGY CHANNEL CodingDecoding

5. 2015. 12. 20. 5 Course objective: algorithmic skills and knowledge (coding procedures) for increasing the performance of communication systems!

6. 2015. 12. 20. 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

7. 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

8. 2015. 12. 20. 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

9. Main parameters of current wireless systems TÁMOP – 4.1.2-08/2/A/KMR-2009-0006 9 2015. 12. 20.

10. Demand vs. Capacity and Spectrum Occupancy 10 2015. 12. 20. TÁMOP – 4.1.2-08/2/A/KMR-2009-0006

11. 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

12. 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 ?

13. 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)

14. Source coding 0000 0001 0010 0011 0100 0101 1111 0000 0001 0010 0011 0100 0101 …………00000000 1 1 1 1 1 …………0 # of bits appr. One-fourth symbolscodewo rds a101 a210111 a3111 a4110 aN01110 Optimal codetable ?

15. Channel coding Unreliable channel 010010110 0110111010 Unreliable channel 00000 5x repeat 0 0 Majority detector 0101001010 What is the optimal code guaranteeing a predefined relaibility with minimum loss of dataspeed?

16. Cryptography Public channel Cypher Decypher message key attacker 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 ?

17. Summary Primer info (voice, image..etc.) Channel Retrieved info Alg. Corrupt recepetion QoS: BER, data rate 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

18. THANK YOU FOR YOR ATTENTION !