The front-end is a crucial component in modern wireless communication systems. For SISO systems minimizing the front-end noise factor is optimal, and this also applies to MIMO systems with i.i.d. noise. However, for compact MIMO receivers that may exhibit spatially correlated noise, e.g., through antenna mutual coupling, the optimal design procedure is not clear. In this paper we develop MIMO low-noise design principles from a communication theory perspective by deriving generalizations of SNR and noise factor from various MIMO communication schemes. As one result, we are able to derive optimal matching networks for a bank of uncoupled amplifiers.