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.