127. linear network coding over rings
Name: Joseph Michael Connelly
Grad Year: 2018
Network coding is a technique which can increase the information throughput of a network by allowing network nodes to transmit functions of their inputs, as opposed to simply relaying received data. Network codes where the functions are linear are of interest due to their mathematical tractability and low implementation complexity. The study of linear network coding has typically been limited to finite field alphabets; however, one can similarly define linear network codes over other structured alphabets, such as finite rings. We contrast linear network codes over fields, commutative rings, and non-commutative rings and additionally discuss cases where none of the above are sufficient. These results show that: (i) it can sometimes be advantageous to consider more general types of linear network codes, and (ii) in some networks, non-linear codes can outperform even very general linear codes.
Industry Application Area(s)
Internet, Networking, Systems