# Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

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Coding Technology

A tantárgy neve magyarul / Name of the subject in Hungarian: Kódolástechnika

Last updated: 2024. február 22.

 Budapest University of Technology and Economics Faculty of Electrical Engineering and Informatics Informatics EngineeringBSc
 Course ID Semester Assessment Credit Tantárgyfélév VIHIAB04 3 3/1/0/v 4
3. Course coordinator and department Dr. Levendovszky János,
4. Instructors Dr. János Levendovszky, professor
5. Required knowledge Introduction to discrete mathematics 1-2
6. Pre-requisites
Kötelező:
(TárgyTeljesítve("BMEVISZAA06") VAGY
TárgyTeljesítve("BMEVISZAA03")) ÉS

NEM ( TárgyTeljesítve("BMEVIHIAB00") ) ÉS

(Kepzes("5N-A8") VAGY
Kepzes("5NAA8"))

VAGY EgyenCsoportTagja("Kreditpótlás_2023/24/2 ")

A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

Ajánlott:
Analysis 1-2
7. Objectives, learning outcomes and obtained knowledge The aim of this course is to describe the main algorithms for the three basic coding tasks involved in the storage and transmission of information. These areas are related to (i) the transmission of information over unreliable communication channels or storage on unreliable storage (error-correcting coding), (ii) the representation of information in a smaller size (data compression, source coding), and (iii) the protection of sensitive information against intelligent attackers when transmitted over public channels (data security, cryptography)
8. Synopsis Error-correcting coding: binary channel model, error probability, basic coding concepts (geometric interpretation, code spacing, optimal codes, code spacing), general coding scheme and its complexity. Singleton and Hamming bounds. Binary linear code, generator matrix, parity check matrix, systematic code. Hamming code, Standard Array. Error correcting performance and relation between column vectors of parity check matrix. Prime and prime-power  size Galois fields, operations on prime-power Galois fields with shift registers. Nonbinary codes, Hamming codes, Reed-Solomon codes. Cyclic linear codes, generator and parity check polynomials. Error trapping algorithm. Minimal polynomials over Galois fields of prime power, BCH codes.
Data compression - source coding: prefix codes, average code word length and entropy. Shannon-Fano code. Binary Huffmann code. Distribution free coding: Adaptive Huffman codes, Lempel-Ziv codes. Predictive coding. Speech and voice compression algorithms. Image and video compression algorithms.
Cryptography – data security: basic concepts: sensitive information and its attack, cryptography (symmetric, asymmetric). Cryptographic techniques, key-stream and block cryptographs. Shift cryptography, polyalphabetic cryptography, affine cryptography, LFSR
based key stream cryptography, DES block cryptography, 3DES and AES ciphers, SSL protocol. OTP algorithm. Fundamentals of number theory. Public key cryptography. The RSA algorithm and its application.

Topics for the practices
Error correcting coding:
Tasks related to binary linear coding, Reed-Solomon codes, code combinations, applications in communication technologies, network coding, QoS communication

Data compression and source coding:
Examples for Huffman, Shannon-Fano, Sahnnon-Fano-Elias for codes, Adaptive Huffman coding, LZ family of algorithms for file compression, Adaptive predictive coding, Transform based compression (KLT and PCA)

Data security coding:
Examples of OTP algorithm, RSA algorithm
9. Method of instruction In lectures: general discussion of coding algorithms,
In practices: applying the theoretical material through numerical examples and real applications.
10. Assessment

During the semester, 1 successful (at least 40%) mid-term test for the signature

Exam    Successful exam  (at least 40%)

 Elégtelen Elégséges Közepes Jó Jeles 0-39 pont 40-53 pont 54-67 pont 68-81 pont 82-100 pont

11. Recaps Retake in the semester and Re-re-take in the catch-up week, retake of the exam
12. Consultations Based on pre-agreed times
13. References, textbooks and resources •    D. Costello: Error control codes, Wiley, 2005
•    S. Verdu, S. Mclaughlin: Information Theory: 50 years of discovery, IEEE, 1999
•    J.G. Proakis: Digital communications,McGraw Hill, 1996
•    T.M. Cover, A.J. Thomas: Elements of Information Theory, John Wiley, 1991. (IT)
14. Required learning hours and assignment
 Contact hours 42 Preparation for practices 18 Preparation for the mid-term test 16 Homework 0 Processing related literature 4 Preparing for the exam 40 Total 120
15. Syllabus prepared by Dr. János  Levendovszky, professor, Department of Networked Systems and Services