Analysis of Overlapped Chunked Codes with Small Chunks over Line Networks

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.