Hierarchical Network Transfer Function and Doubly-Greedy Half-Duplex Stage Scheduling for WPNC Networks

Wireless Physical Layer Network Coding (WPNC) based communication networks deliver the information from sources to destinations through the complex relay network. To properly design the Network Coded Modulation transmitted by network nodes and the relay processing including the Hierarchical Network Code (HNC) maps, we need a formal description of the global network processing function. Any practical implementation also implies the half-duplex constrained relays which imposes the network to work in multiple stages. We present a polynomial based formalism defining the Hierarchical Network Transfer Function (H-NTF). It captures all phenomena related to the stage dependent transmit and receive activity over the network, including potential buffering, and mainly the hierarchy of forming the local HNC maps into the global hierarchical flow description. Using the polynomial formalism of H-NTF, we develop the half-duplex constrained stage scheduling algorithm. It starts with finding a causal minimal latency (or close to minimal) critical sequence with subsequent doubly (first Rx then Tx) greedy mapping of the node activity compliant with the half-duplex constraint.