Residual packet loss rate analysis of 2-D parity forward error correction

To improve the robustness of video communications over IP networks against packet losses, numerous IPTV and broadcasting standards have adopted the 2D application-layer forward error correction (FEC) method presented in Pro-MPEG COP3. This method uses a two-dimensional encoding matrix in which redundant checksums for each row and each column of the data matrix are generated and transmitted with the data packets. The approach has been recently extended and applied to layered video streaming. But despite its wide adoption and importance, a formal analysis of the correction performance of the Pro-MPEG COP3's 2D FEC method is still lacking. In this paper, we formulate and solve the problem using an abstract mathematical framework, which can be used also for some natural extensions of this method. We derive tight bounds on the residual packet loss rate as a function of the 2D FEC matrix dimensions, and the packet loss rate assuming that the losses are independently and randomly distributed. We then provide simple approximations on these bounds for low packet loss rates. The analysis leads to the observation that the addition of a single checksum packet to the Pro-MPEG COP3 method would lead to a significant reduction in residual packet loss rate. The expressions derived are validated experimentally using Monte Carlo simulations. We also apply the results to the case of packet losses occurring in bursts. Finally, we study the impact of the matrix dimensions on the performance of the 2D FEC method, leading to valuable recommendations to system designers.