Mrežno kodiranje

master's thesis

• Author: Karlo Nikoletić
• Mentor: Vedran Krčadinac (mentor)
• Committee member: Vedran Krčadinac (predsjednik povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Tomislav Pejković (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu obrađene su metode prijenosa informacija kroz komunikacijski kanal. Proučene su metode klasičnog kodiranja i mrežnog kodiranja. U klasičnom kodiranju smo definirali blokovne kodove te njihova svojstva. Također smo definirali linearne kodove i proučili dvije vrste, Hammingove i Reed-Mullerove kodove. Nakon toga smo obradili mrežno kodiranje kod kojeg se paketi linearno kombiniraju na čvorovima. Glavna tvrdnja rada je da se u mrežnom kodiranju jednakom brzinom, kojom u klasičnom kodiranju prenosimo informaciju na jedno odredište, može prenijeti informacija na više odredišta. Tvrdnju iskazujemo i dokazujemo glavnim teoremom mrežnog kodiranja u čijem dokazu se koristi teorem minimalnog reza i maksimalnog toka. Na kraju smo obradili vrstu mrežnog kodiranja u kojem se paketi nasumično linearno kombiniraju na čvorovima, slučajno mrežno kodiranje i odgovarajuće potprostorne kodove.

Abstract (english)

In this graduate thesis, methods of information transfer through the communication channel were discussed. Classical coding and network coding methods were studied. In classical coding, we have defined block codes and their properties. We also defined linear codes and studied two types, Hamming and Reed-Muller codes. After that, we discussed network coding in which packets are linearly combined at the nodes. The main claim of the thesis is that in network coding at the same speed, at which in classical coding we transfer information to one destination, information can be transferred to several destinations. We state and prove the claim by the main network coding theorem in the proof of which the theorem of minimum cut and maximum ow is used. Finally, we discussed a type of network coding in which packets are randomly linearly combined at the nodes, random network coding and the corresponding subspace codes.

• Keywords: prijenos informacija; komunikacijski kanal; klasično kodiranje; mrežno kodiranje; linearni kodovi; Hammingovi kodovi; Reed-Mullerovi kodovi
• Keywords (english): information transfer; communication channel; classical coding; network coding; linear codes; Hamming codes; Reed-Muller codes
• Language: croatian
• URN:NBN: urn:nbn:hr:217:357451
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-11-26 13:04:51