Two-Unicast Two-Hop Interference Network: Finite-Field Model

In this paper we present a novel framework to convert the $K$-user multiple access channel (MAC) over $\FF_{p^m}$ into the $K$-user MAC over ground field $\FF_{p}$ with $m$ multiple inputs/outputs (MIMO). This framework makes it possible to develop coding schemes for MIMO channel as done in symbol extension for time-varying channel. Using aligned network diagonalization based on this framework, we show that the sum-rate of $(2m-1)\log{p}$ is achievable for a $2\times 2\times 2$ interference channel over $\FF_{p^m}$. We also provide some relation between field extension and symbol extension.