Kodiranje koje ispravlja greške

master's thesis

• Title (english): Error correcting coding
• Author: Šime Gaurina
• Mentor: Filip Najman (mentor)
• Committee member: Marko Erceg (predsjednik povjerenstva)
• Committee member: Zrinka Franušić (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-03-06, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj ovoga rada je opisati kodiranja koja ispravljaju greške. U prvom poglavlju su opisani osnovni pojmovi kod kodiranja koja ispravljaju greške i dan je jedan jednostavni primjer kodiranja. U drugom poglavlju se opisuje Hammingov (7, 4) kod i definira se Hammingova udaljenost. U trećem poglavlju opisuju se blok kodovi, tj. kodovi u kojima se podatci dijele na blokove. Također je dana gornja granica na broj kodnih riječi. Opisani su savršeni kodovi i definiran pojam ekvivalentnosti kodova. Opisan je i Hammingov (8, 4) kod koji detektira dvije pogreške u prijenosu poruke. U četvrtom poglavlju su opisani linearni kodovi i dana je definicija dviju važnih matrica: generirajuće matrice i matrice provjere pariteta. Opisano je kako pomoću njih dobiti enkodiranu riječ, odnosno kako provjeriti pripada li riječ kodu. U istom poglavlju su opisane i neke metode dekodiranja poruke. U petom poglavlju se formaliziraju Hammingovi kodovi. Opisani su i simpleks kodovi te Hadamardovi kodovi.

Abstract (english)

The goal of this paper is to describe error-correcting codes. In the first chapter, the basic concepts of error-correcting codes are described and a simple example is given. In the second chapter, the Hamming (7, 4) code is described and the Hamming distance is defined. In the third chapter, block codes are described, i.e. codes in which data is divided into blocks. In the same chapter, the upper limit for the number of codewords is given. Perfect codes are described and the concept of code equivalence is defined. The Hamming (8, 4) code, which detects two errors in message transmission is described. In the fourth chapter, linear codes are described and two important matrices are defined: generator matrix and parity check matrix. It is described how to use them to encode a word and how to check whether the word belongs to the code. In the same chapter, some methods of message decoding are described. In the fifth chapter, Hamming codes are formalized. Simplex codes and Hadamard codes are also described.

• Keywords: Hammingova udaljenost; blok kodovi; savršeni kodovi; linearni kodovi; generirajuća matrica; matrica provjere pariteta; enkodirana riječ; Hammingovi kodovi; Hadamardovi kodovi
• Keywords (english): Hamming distance; block codes; perfect codes; linear codes; generating matrix; parity check matrix; encoded word; Hamming codes; Hadamard codes
• Language: croatian
• URN:NBN: urn:nbn:hr:217:310663
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-27 07:45:30