Analog network coding mappings in Gaussian multiple-access two-hop channels

We consider the multiple-access two-hop channel where two source nodes transmit to a destination node via a relay node. The relaying function is memoryless, in contrast to the conventional schemes based on coding with long codewords. That is, we model the operation of the relay as a two-to-one deterministic mapping, which combines the two received analog signals from the sources. This procedure resembles the concept of network coding where information combining is applied in the intermediate nodes. However, as our mapping directly combines the received analog signals without decoding, we coin the term (memoryless) analog network coding mapping. In this paper, both linear and non-linear mappings are studied. In particular, the Archimedean spiral is used for the non-linear 2:1 mapping, inspired by similar work in the context of joint source-channel coding. We discuss both the achievable rate regions and sum rates and demonstrate significant gains of applying the proposed analog mappings in the relay.