Modulo-Type Precoding for Networks

In this chapter, we address scenarios where the tasks of (modulo-type) precoding for the multiple-input/multiple-output (MIMO) broadcast channel, network coding with its associated finite-field matrix channel, and channel coding meet or complement each other. By enlightening dualities, similarities, and differences between the areas and corresponding schemes, a deeper understanding of theirmutual interaction is gained. Moreover, this allows for a transfer of schemes and strategies from one field to another one. Exemplarily, schemes operating at the intersection of complex-valued and finite-field/modulo processing are addressed. First, an overview onmodulo-type precoding and its latest version via finite-field preprocessing is given; the connections and specific restrictions of the different approaches are illustrated. The advantages of modulo-type precoding are addressed when additional requirements, such as per-antenna power constraints and a reduced degree of coordination in a network MIMO scenario, are imposed. Finally, the application of precoding to finite-field channels is discussed, either as differential network coding or as selection precoding.