Funktsiooni arvutus võrkudes
Date
2017
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Abstract
Ruutimine, mis kasutab ainuüht parimat teekonda sõnumite edastamiseks, on praegusel hetkel peamine meetod informatsiooni edastamiseks võrgus. Väljapakutud alternatiiviks on võrgukodeerimine, mis lubab kogu võrgul osaleda informatsiooni edastamises, saates kodeeritud infot läbi mitme teekonna ja taastades algse sõnumi vastuvõtjas. Mõningate rakenduste korral on algsete sõnumite taastamise asemel vaja funktsiooni üle nende sõnumite. Nimetame seda funktsiooni arvutuseks võrgus. Selline lähenemine lubab arvutusi teha teekonna jooksul, mil sõnum liigub allikatest saajateni. See töötab hästi näiteks võrkudes, kus ühendatud on palju piiratud arvutusvõimsusega väikseid seadmeid. Situatsioon, mis IoT esiletõusuga ilmneb aina tihedamini. Kuna funktsiooni arvutus võrkudes on suhteliselt uus mõiste, ei ole veel täiesti suudetud mõista võrgu funktsionaalarvutuse rakendatavust ja teoreetilise jõudlikkuse piire.Käesolev töö keskendub kindlale sihtfunktsioonide perekonnale ja tuvastab võrgu omadusi, et funktsionaalarvutus oleks edukas. See töö esitab kodeerimislahendusi, mis lubavad edukalt võrgus funktsionaalarvutusi läbi viia, kus sõnumiteks on üksikud sümbolid. Tulemused on seejärel laiendatud suvalise sümbolite arvuga sõnumitele, kasutades sarnast kodeerimislahendust.
Routing, that uses a single best path in the network, is currently the primary method for information transfer in networks. A proposed alternative to routing is called network coding that allows for the whole network to participate in the transmission of information by sending the coded data using multiple paths and then reconstructing the original message at the receiver. In some applications instead of reconstructing the original messages a function of those messages needs to be obtained. The corresponding problem is called a problem of function computation in the network. This approach allows for efficient en-route computing that works especially well with many small connected devices with limited computational capacities, a situation that appears often with the rise of the IoT. Since network function computation is a relatively new concept, the applicability and theoretical performance limits of this approach are not yet fully understood. The current work focuses on a certain family of target functions and identifies properties a network must have for function computation to be feasible. We propose encoding solutions that allow for successful network function computation. The results are then extended to packets with arbitrary number of symbols using a similar encoding scheme.
Routing, that uses a single best path in the network, is currently the primary method for information transfer in networks. A proposed alternative to routing is called network coding that allows for the whole network to participate in the transmission of information by sending the coded data using multiple paths and then reconstructing the original message at the receiver. In some applications instead of reconstructing the original messages a function of those messages needs to be obtained. The corresponding problem is called a problem of function computation in the network. This approach allows for efficient en-route computing that works especially well with many small connected devices with limited computational capacities, a situation that appears often with the rise of the IoT. Since network function computation is a relatively new concept, the applicability and theoretical performance limits of this approach are not yet fully understood. The current work focuses on a certain family of target functions and identifies properties a network must have for function computation to be feasible. We propose encoding solutions that allow for successful network function computation. The results are then extended to packets with arbitrary number of symbols using a similar encoding scheme.