Carry-free models and beyond

The generalized deterministic models recently proposed by Niesen and Maddah-Ali [1] successfully capture real-interference alignment as observed in Gaussian models. Simpler deterministic models, like ADT models [2], cannot demonstrate this phenomenon because they are limited in the set of channel gains they can model. This paper reinterprets the Niesen and Maddah-Ali models through the lens of carry-free operations. We further explore these carry-free models by considering i.i.d. unknown fading networks. In the unknown fading context, a carry-free model can be further simplified to a max-superposition model, where signals are superposed by a nonlinear max operation. Unlike in relay-networks with known fading and linear superposition, we find that decode-and-forward can perform arbitrarily better than compress-and-forward in max-superposition relay networks with unknown fading.