Finite blocklength performance of multi-hop relaying networks

In this paper, we study the performance of a multi-hop relaying network with finite blocklengths under quasi-static Rayleigh fading channels. The throughputs under the assumption of infinite blocklengths (IBL-throughput) as well as under the assumption of finite blocklengths (FBL-throughput) are studied, respectively. In particular, the FBL-throughput is considered under two scenarios, i.e., either with target overall error probability or with constant coding rate. By numerical analysis, we investigate the FBL-throughput and compare it with the IBL-throughput. We find that there exists an optimal number of hops maximizing the corresponding throughput under either the IBL or the FBL assumptions, while these optimal number of hops are different under these two assumptions. Moreover, we show that the FBL-throughput is quasi-concave in the overall error probability under the target overall error probability scenario, which is also quasi-concave in the coding rate under the constant coding rate scenario. In addition, it is shown that the influences of blocklength on FBL-throughputs under these two scenarios are different, e.g., the performance of multi-hop relaying with target overall error probability is more sensitive to the blocklength in comparison to the constant coding rate scenario.