Sliding Window-Based Erasure Correction Using Biased Sampling

We study a packet erasure correction method based on biased sampling in a sliding window. This kind of coding works especially well for streaming data, where the data have real-time requirements and expire after sometime. The coding method resembles fountain coding but we allow biased sampling of the source blocks inside the window. We present an exact Markov model for analyzing the erasure correction performance and use Wallenius´ noncentral hypergeometric distribution for calculating the erasure correction probability of a specified sampling pattern. The model is derived for independent packet erasures, and the sender is assumed to have an estimate on the erasure probability. We truncate the state space in order to lower the computational complexity by limiting the number of allowable erasures within the window, and study scenarios with low channel erasure probability and small window size. The optimal sampling weights are searched and the results suggest that a deterministic sampling pattern isoptimal in the depicted scenario. A comparison to state-of-the-art Raptor codes for a similar setting reveals improved erasure correction performance with the proposed method.