  We assess the practicality of random network coding by illuminating the issue
of overhead and considering it in conjunction with increasingly long packets
sent over the erasure channel. We show that the transmission of increasingly
long packets, consisting of either of an increasing number of symbols per
packet or an increasing symbol alphabet size, results in a data rate
approaching zero over the erasure channel. This result is due to an erasure
probability that increases with packet length. Numerical results for a
particular modulation scheme demonstrate a data rate of approximately zero for
a large, but finite-length packet. Our results suggest a reduction in the
performance gains offered by random network coding.
