The objective of low-delay codes is to protect communication streams from erasure bursts by minimizing the time between the packet erasure and its reconstruction. Previous work has concentrated on the constant-delay scenario, where all erased packets need to exhibit the same decoding delay. We consider the case of heterogeneous delay, where the principal objective is to minimize the average delay across the erased packets in a burst. This new model is motivated by communications in sense and control networks.
In the thesis we:
1) Derive delay lower bounds for the average case, and show that they are strictly lower than the constant-delay bounds for all rates except the single rate point 0.5.
2) Construct codes with optimal average delays for the entire range of code rates. The construction for rates under 0.5 achieves optimality for every erasure instance, while the constructions for rates above 0.5 are optimal for an infinite number, but not all, of the erasure instances.
3) Show natural applications and matching heterogeneous-delay constructions. We focus on the scenario of packets with a significance hierarchy. Our suggested construction enables a faster recovery of packets with a higher significance level.