  This paper investigates adaptive streaming codes over a three-node relayed
network. In this setting, a source node transmits a sequence of message packets
to a destination through a relay. The source-to-relay and relay-to-destination
links are unreliable and introduce at most $N_1$ and $N_2$ packet erasures,
respectively. The destination node must recover each message packet within a
strict delay constraint $T$. The paper presents achievable streaming codes for
all feasible parameters $\{N_1, N_2, T\}$ that exploit the fact that the relay
naturally observes the erasure pattern occurring in the link from source to
relay, thus it can adapt its relaying strategy based on these observations. In
a recent work, Fong et al. provide streaming codes featuring
channel-state-independent relaying strategies. The codes proposed in this paper
achieve rates higher than the ones proposed by Fong et al. whenever $N_2 >
N_1$, and achieve the same rate when $N_2 = N_1$. The paper also presents an
upper bound on the achievable rate that takes into account erasures in both
links in order to bound the rate in the second link. The upper bound is shown
to be tighter than a trivial bound that considers only the erasures in the
second link.
