A Multilevel Framework for Lattice Network Coding

We present a general framework for studying the multilevel structure of lattice network coding (LNC), whichserves as the theoretical fundamental for solving the ring-based LNC problem in practice, with greatly reduceddecoding complexity. Building on the framework developed, we propose a novel lattice-based network codingsolution, termed layered integer forcing (LIF), which applies to any lattices having multilevel structure. Thetheoretic foundations of the developed multilevel framework lead to a new general lattice construction approach, theelementary divisor construction (EDC), which shows its strength in improving the overall rate over multiple accesschannels (MAC) with low computational cost. We prove that the EDC lattices subsume the traditional complexconstruction approaches. Then a soft detector is developed for lattice network relaying, based on the multilevelstructure of EDC. This makes it possible to employ iterative decoding in lattice network coding, and simulationresults show the large potential of using iterative multistage decoding to approach the capacity.