  This paper investigates adaptive streaming codes over a three-node relayed
network. In this setting, a source transmits a sequence of message packets
through a relay under a delay constraint of $T$ time slots per packet. The
source-to-relay and relay-to-destination links are unreliable and introduce a
maximum of $N_1$ and $N_2$ packet erasures respectively. Recent work has
proposed adaptive (time variant) and nonadaptive (time invariant) code
constructions for this setting and has shown that adaptive codes can achieve
higher rates. However, the adaptive construction deals with many possibilities,
leading to an impractical code with very large block lengths. In this work, we
propose a simplified adaptive code construction which greatly improves the
practicality of the code, with only a small cost to the achievable rates. We
analyze the construction in terms of the achievable rates and field size
requirements, and perform numerical simulations over statistical channels to
estimate packet loss probabilities.
