Analysis of Overlapped Chunked Codes with Small Chunks over Line Networks

TL;DR

This paper demonstrates that overlapped chunked codes with small chunks can asymptotically achieve network capacity, with larger overlaps improving convergence speed and error rates, making OCC suitable for multimedia transmission.

Contribution

The paper proves that small-chunk CC and OCC approach capacity and shows that larger overlaps enhance performance, highlighting OCC's advantages for short chunks.

Findings

Small chunks asymptotically approach capacity.

Larger overlaps improve convergence and error rates.

Simulations confirm theoretical advantages for multimedia applications.

Abstract

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.