We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a finite field. In this context, we establish an outer bound for the achievable rate region and provide examples of networks where the bound is sharp. We finally give evidence of the crucial role played by the field characteristic in the problem.

翻译：我们提出了一个形式化框架，用于研究编码网络中的多单播问题，其中网络编码在有限域上线性且固定。我们证明该问题对应于有限域上的干扰对齐问题。在此背景下，我们建立了可达速率域的外界，并给出了该界紧致的网络示例。最后，我们论证了域特征在该问题中的关键作用。