Two-unicast two-hop interference network: Finite-field model

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