Network coding

Linear network coding is a mathematical technique which may be used to improve a network's throughput, efficiency and scalability, as well as resilience to attacks and eavesdropping. Instead of simply relaying the packets of information they receive, the nodes of a network take several packets and combine them together for transmission. This may be used to attain the maximum possible information flow in a network.

It has been proven in theory that linear coding is enough to achieve the upper bound in multicast problems with one source. However linear coding is not sufficient in general (e.g. multisource, multisink with arbitrary demands), even for more general versions of linearity such as convolutional coding and filter-bank coding. Finding optimal coding solutions for general network problems with arbitrary demands remains an open problem.

In a linear network coding problem, a group of nodes ${\displaystyle P}$ are involved in moving the data from ${\displaystyle S}$ source nodes to ${\displaystyle K}$ sink nodes. Each node generates new packets which are linear combinations of earlier received packets, multiplying them by coefficients chosen from a finite field, typically of size ${\displaystyle GF(2^{s})}$.

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