Iterative Double-Loop Hierarchical Decoding with Soft-Aided Bit-Wise H-SODEM in WPNC Networks

This paper addresses Wireless Physical Layer Network (WPNC) coding using Isomorphic Layered Network Coded Modulation (NCM) in hierarchical MAC stage with Hierarchical Decode and Forward (HDF) strategy. We focus on using binary component codes in bit-wise mapped higher-order hierarchical constellations and on the way how to improve the outer code iterative decoding. Soft bit-wise hierarchical decoding metric exhibits two important properties. (1) Unlike the single-user case, the hierarchical metric is many-to-one function of message symbols and even for perfect a priori soft-information, it contains hierarchical self-dispersion. (2) The bit-wise mapping itself creates a complicated nonlinear block-like inter-bit structure binding and the bit-wise observation model cannot be any longer described by single-letter entities. It also strongly depends on the source constellation bit mapping, actual bit-wise a priori PMFs, and also on the actual relative channel parametrization. We derive bit-wise soft-aided Hierarchical Soft-Output Demodulator (H-SODEM). We show how to cope with self-dispersion in specific cases. We analyze the bit error rate properties of the dual-loop soft-aided bit-wise hierarchical decoding in 2-source H-MAC HDF scenario and show significant performance improvement w.r.t. classical uniform a priori case.