Selection Precoding for the Finite-Field Multiplicative Matrix Channel

The finite-field multiplicative matrix channel is a well suited model for random linear network coding in the absence of packet errors and for lattice-coded MIMO transmission utilizing "integer forcing" receivers or transmitters. In this letter, modulo-type precoding for such channels is proposed. Thereby, the channel is not only equalized but by selecting a suited candidate, desired properties of the transmit symbols can be achieved. The operation of selection precoding is explained and its performance is analyzed and demonstrated.