On capacity regions of non-multicast networks

We study the network coding capacity of multi-source, multi-sink networks with colocated sources, but where each sink may demand a different subset of the sources. We show that in this scenario, the set of admissible (zero probability of decoding errors) and achievable (vanishing probability of decoding errors) rate capacity tuples are the same. We also simplify the capacity region by showing that the outer bound obtained in “A First Course in Information Theory” (Yeung, 2002) is in fact tight. We conjecture that this bound remains tight, even when the sources are not colocated.