# 455-0919/01 – Coding and Cryptography Applications ()

 Gurantor department Department of Measurement and Control Credits 0 Subject guarantor prof. Ing. Karel Vlček, CSc. Subject version guarantor prof. Ing. Karel Vlček, CSc. Study level postgraduate Requirement Choice-compulsory Year Semester winter + summer Study language Czech Year of introduction 1960/1961 Year of cancellation 2005/2006 Intended for the faculties FEI Intended for study types Doctoral
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Part-time Credit and Examination 2+0

### Summary

Theoretical basics of discipline "Multimedia Data Processing" are formed in the two Shannon theorems. The first theorem on coding without the error occurring forms the conditions of data compression. The key variable is entropy of source of messages or in other words the amount of redundancy in the message or data set. Entropy is a criterion for decision of the compression type. The compression will be without lost of information, if the value of entropy is not exceed, and it is with the lost of information if it is exceed. The second theorem is called on coding with the error occurring. This theorem is formed as conditions of error-control coding, which differ in the way of encoding and decoding calculation. The error occurring in the records is defined by conditions of physical properties of memory medium. The explanations are defined in general mathematical form, and it is abstracted from the fact, if the medium is the communication channel or memory. It is necessary to consider the both characters of media properties in the praxis. The course is streamed to practical and effective processing of multimedia data in databases. Due to it interests in modern technologies based on the optical principles. These technologies are typical by the burst-errors. It is the reason for application the codes with non-binary alphabet as well as convolution codes. These methods are necessary for use in another applications, namely in error-control methods of video signal. The special chapter on the end of course on error-control coding is introduced so called turbo-codes, which are used in radio transmission of data and are considered as the new trend for producers of mobile devices of UMTS generation. Necessary part of data processing is its protection against enemy. The basic methods of ciphering of data are introduced in overview.

### Way of continuous check of knowledge in the course of semester

Průběžná kontrola studia: Zpracování samostatného projektu

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Přednášky: Vznik teorie informace a kódování. Základní pojmy kódování. Zpráva. zdrojová abeceda. Prefixové kódování. Kraftova nerovnost. McMillanova věta. Huffmanovy kódy. Pojem entropie. Shannonovy věty. Sdělovací kanály. Konstrukce Hammingových kódů. Opravy jednoduché chyby. Příklady dekodérů Hammingových kódů. Golayův kód. Reedovy - Müllerovy kódy. Booleovské funkce a polynomy. Dekódování Reedových - Müllerových kódů. Opakovací kódy. Kódy prvního řádu. Obecné Reedovy - Müllerovy kódy. Cyklické kódy. Operace s polynomy. Zbytek dělení. Generující polynom. Kontrolní polynom. Konečná tělesa a polynomy. BCH - kódy pro dvojnásobné a trojnásobné opravy. Maticová metoda dekódování, určení syndromu a lokátoru chyb. Reedovy - Solomonovy kódy. Kód s plánovanou vzdáleností d. BCH - kód délky q-1. Dekódování BCH - kódu. Lokátor a evaluátor chyb, provedení opravy. Konvoluční kódy. Kódování konvolučních (n,1)-kódů. Dekódování konvolučních kódů. Viterbiho algoritmus dekódování. Kódování tajných zpráv. Jednorázový klíč. Simplexový kód. Pseudonáhodná slova. Reedův - Müllerův kód R(1,3). Šifrování veřejně přístupným klíčem. Metoda velkých prvočísel; provádění metody. Metoda založená na zavazadlovém problému. Aplikace kódů v telekomunikační technice.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (145) 51
Examination Examination 100  0
Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2005/2006 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2004/2005 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2003/2004 (P2646) Information Technology (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (1801V002) Computer Science and Applied Mathematics P Czech Ostrava Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner