20.500.12556/RUL-102701 Uvod v teorijo informacij delo diplomskega seminarja Introduction to information theory V delu diplomskega seminarja sem se ukvarjal z iskanjem kodiranja, ki ima najmanjšo pričakovano dolžino. Takšnemu kodiranju pravimo optimalno kodiranje. Najprej sem določil omejitve dolžin optimalnega kodiranja in dokazal Kraftovo neenakost za predponska kodiranja in kodiranja, ki se jih da enolično odkodirati (enolična kodiranja). Kraftova neenakost nam namreč daje potreben in zadosten pogoj za obstoj predponskega kodiranja ali enoličnega kodiranja za dano množico dolžin. V zaključku dela pa sem se osredotočil na Huffmanovo kodiranje. Na primerih sem predstavil idejo Huffmanovega algoritma ter povezave z nekaterimi drugimi matematičnimi problemi. Nato sem podal teoretično ozadje algoritma in dokazal, da je kodiranje, ki ga dobimo s Huffmanovim algoritmom, optimalno. In the course of the diploma seminar I was looking for code with the smallest expected length. Such code is called optimal code. First I defined the limits of lengths of optimal code and presented Kraft inequality for prefix code and uniquely decodable code. Kraft inequality gives us a necessary and sufficient condition for the existence of a prefix code or a uniquely decodable code for a given set of codeword lengths. At the end of my work I focused on Huffman codes. Using examples I presented the idea of Huffman algorithm and the connection with some other mathematical problems. Then I gave the theoretical background to the algorithm and concluded that the code obtained with the Huffman algorithm is optimal. entropija Huffman informacija koda kodiranje Kraftova neenakost optimalno Shannon entropy Huffman information codeword code Kraft inequality optimal Shannon true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2018-09-07 07:45:27 2018-09-07 07:45:34 2022-08-15 03:43:26 0000-00-00 00:00:00 2018 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.8 89410 18429529 211.pdf 211.pdf 1 52E07FF3148E25EF65DF5C32FB5B9BEB 41853349bccc4e57397f65c96eedad0411c830c6deddb2b0f8fe782bef124a78 98fb5f10-a1b5-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=113058 Fakulteta za matematiko in fiziko 0 0 0