On capacity of Gaussian ´cheap´ relay channel

In this paper, we derive the capacity of the Gaussian degraded ´cheap´ relay channel, consisting of nodes using ´cheap´ radios operating in TDD mode when transmitting and sending in the same frequency band. The TDD model captures a practical limitation of most of the RF radios used in commercial wireless systems. The proof of achievability relies on a combination of superposition encoding and list decoding, while the converse is derived using the min-cut max-flow theorem for networks with ´cheap´ nodes (previously derived by the authors). Even with ´cheap´ radios, our capacity analysis shows that cooperative coding is beneficial and has a capacity advantage over direct transmission.