  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.
