Blocklength-Limited Performance of Relaying under Quasi-Static Rayleigh   Channels
  In this paper, the blocklength-limited performance of a relaying system is studied, where channels are assumed to experience quasi-static Rayleigh fading while at the same time only the average channel state information (CSI) is available at the source. Both the physical-layer performance (blocklength-limited throughput) and the link-layer performance (effective capacity) of the relaying system are investigated. We propose a simple system operation by introducing a factor based on which we weight the average CSI and let the source determine the coding rate accordingly. In particular, we prove that both the blocklength-limited throughput and the effective capacity are quasi-concave in the weight factor. Through numerical investigations, we show the appropriateness of our theoretical model. In addition, we observe that relaying is more efficient than direct transmission. Moreover, this performance advantage of relaying under the average CSI scenario is more significant than under the perfect CSI scenario. Finally, the speed of convergence (between the blocklength-limited performance and the performance in the Shannon capacity regime) in relaying system is faster in comparison to the direct transmission under both the average CSI scenario and the perfect CSI scenario. 
Yulin Hu, Anke Schmeink and James Gross
cs.IT math.IT