  Under the assumption of outdated channel state information (CSI) at the
source, we consider the finite blocklength (FBL) throughput of a two-hop
relaying system. Previous work has considered this setting so far only for the
infinite blocklength case, where decoding can be arbitrarily reliable as long
as operating below the Shannon limit. In contrast, in the FBL regime residual
decoding errors can not be avoided even when transmitting below the Shannon
limit. This makes the scheduling problem at the source more vulnerable to
transmission errors, where we investigate the trade-off between the choice of
so called scheduling weights to avoid transmission errors and the resulting
coding rate. We show that the corresponding maximization of the throughput
under a reliability constraint can be solved efficiently by iterative
algorithms. Nevertheless, the optimal solution requires a recomputation of the
scheduling weights prior to each transmission. Thus, we also study heuristics
relying on choosing the scheduling weights only once. Through numerical
analysis, we first provide insights on the structure of the throughout under
different scheduling weights and channel correlation coefficients. We then turn
to the comparison of the optimal scheduling with the heuristic and show that
the performance gap between them is only significant for relay systems with
high average signal-to-noise ratios (SNR) on the backhaul and relaying link. In
particular, the optimal scheduling scheme provides most value in case that the
data transmission is subject to strict reliability constraints, justifying the
significant additional computational burden.
