  To lower the complexity of network codes over packet line networks with
arbitrary schedules, chunked codes (CC) and overlapped chunked codes (OCC) were
proposed in earlier works. These codes have been previously analyzed for
relatively large chunks. In this paper, we prove that for smaller chunks, CC
and OCC asymptotically approach the capacity with an arbitrarily small but
non-zero constant gap. We also show that unlike the case for large chunks, the
larger is the overlap size, the better would be the tradeoff between the speed
of convergence and the message or packet error rate. This implies that OCC are
superior to CC for shorter chunks. Simulations consistent with the theoretical
results are also presented, suggesting great potential for the application of
OCC for multimedia transmission over packet networks.
