Reliable versus unreliable transmission for energy efficient transmission in relay networks

A network code is said to be reliable when all transmissions in the network are (deterministic) functions of the source messages; well-known examples include decode-forward for relay networks. It is said to be unreliable when transmissions depend on the noise realization at nodes; examples include compress-forward and amplify-forward. The deterministic capacity of a network is defined as the supremum of the rates achievable by reliable codes. In this paper we derive the deterministic capacity of some relay networks in the low power regime. The resulting energy per bit is then compared with the one achievable by arbitrary transmission.