Modul:   MAT075  Zurich Graduate Colloquium

What is... Network Coding?

Vortrag von Beatrice Toesca di Castellazzo

Datum: 29.10.24  Zeit: 16.30 - 17.30  Raum:

Suppose you want to send a message to your friend. Can errors occur during the transmission? Unfortunately yes. It is then crucial to find ways to detect errors in the received message and possibly correct it. The goal of algebraic coding theory is to design ways of encoding messages (vectors over a finite field) with an algebraic structure that guarantees that, with a limited number of errors, the meaning of the original message is not compromised. In multi-cast communication, as in the streaming of data over the Internet, one deals with sending information to multiple receivers across a network with several intermediate nodes. To improve the network throughput, a coding technique called random linear network coding was developed. In this scenario, the intermediate nodes transmit a random linear combination of the vectors received. With this technique, it is possible to asymptotically achieve the maximum capacity of the network, without relying on its topology. In this talk, we will start studying the basic notions of coding theory with only one sender and one receiver, and then switch to the case of data transmission over a network and explain how in this case giving the messages the structure of a linear subspace helps correcting errors.