Network coding is a method of transmitting messages through a network in which intermediate vertices may send functions of received messages instead of merely forwarding them. A linear network code uses linear combinations over a finite field. Coding must respect the capacities of the edges and allow each destination to recover its requested message.
The Li-Li conjecture proposed that such coding cannot improve the common rate for independent multiple-unicast demands in an undirected network. Braverman and He (2026) and Zhang et al. (2026) reported counterexamples.
