Reed-Solomonovi kodovi

master's thesis

• Title (english): Reed-Solomon codes
• Author: Sebastian Taras
• Mentor: Anamari Nakić (mentor)
• Committee member: Anamari Nakić (predsjednik povjerenstva)
• Committee member: Andrea Aglić Aljinović (član povjerenstva)
• Committee member: Domagoj Kovačević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2024-07-03, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing

Abstract

U ovom radu opisani su osnovni matematički postupci vezani za Reed-Solomonove kodove s naglaskom na kodove definirane nad proširenjem polja GF(2). Opisani su postupci aritmetike konačnog polja nad elementima polja te nad polinomima definiranim nad istim poljem te postupak generiranja i primjeri korištenja logaritamskih tablica. Opisana je hijerarhija koda i njegovi parametri. Opisani su postupci kodiranja poruke i postupak dekodiranja poruke, a opisani postupci potkrijepljeni su primjerom kodiranja i dekodiranja poruke. Primjena i vizualizacija Reed-Solomon koda RM(255,223) implementirana je u web aplikaciji za kodiranje slike i teksta s interaktivnim postavljanjem i ispravljanjem grešaka.

Abstract (english)

This thesis explains the mathematical foundation of Reed-Solomon codes, with a focus on the codes defined over extensions of the field GF(2). In the thesis we define mathematical operations of finite field arithmetics over the field's elements as well as polynomials with coefficients in the said fields. We define lookup tables and how to use them to speed up the calculations. We describe the hierarchy and the parameters of Reed-Solomon codes, as well as the encoding and decoding procedurees with examples. The implementation of Reed-Solomon code RM(255,223) is done in a web aplication which allows the user to encode text or image and then create and correct the errors.

• Keywords: Reed-Solomon; Reed-Solomonovi kodovi; zaštitno kodiranje; ciklički kodovi; polinomski kodovi; teorija kodiranja; aritmetika konačnog polja; galoisova polja
• Keywords (english): Reed-Solomon; Reed-Solomon codes; error correcting codes; cyclic codes; polynomial codes; coding theory; finite field aithmetic; galois fields
• Language: croatian
• URN:NBN: urn:nbn:hr:168:323231
• Study programme: Title: Computing; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka računarstva (magistar/magistra inženjer/inženjerka računarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2024-10-12 22:20:03