Jovan StosicNetwork coding is a field of research founded in a series of papers from the late 1990s to the early 2000s. However, the concept of network coding, in particular linear network coding, appeared much earlier. In a 1978 paper, a scheme for improving the throughput of a two-way communication through a satellite was proposed. In this scheme, two users trying to communicate with each other transmit their data streams to a satellite, which combines the two streams by summing them modulo 2 and then broadcasts the combined stream. Each of the two users, upon receiving the broadcast stream, can decode the other stream by using the information of their own stream.
The 2000 paper gave the butterfly network example (discussed below) that illustrates how linear network coding can outperform routing. This example is equivalent to the scheme for satellite communication described above. The same paper gave an optimal coding scheme for a network with one source node and three destination nodes. This is the first example illustrating the optimality of convolutional network coding (a more general form of linear network coding) over a cyclic network.
Linear network coding 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 mathematically 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.[4] Finding optimal coding solutions for general network problems with arbitrary demands remains an open problem.