Correcting erasure bursts with minimum decoding delay

Abstract

Erasure correcting codes are widely used in upper layers of packet-switched networks, where the packet erasures often exhibit bursty patterns. The conventional wisdom to deal with bursty erasures is to apply block interleaving to break down the bursty patterns prior to error correcting coding, or use long-block Reed-Solomon codes. We show that they unnecessarily lead to sub-optimal decoding delay. In this work, with the problem model of multiple erasure bursts present in a coding block, we study the fundamental tradeoff among the rate, decoding delay and burst correction performance of erasure correcting codes. Focusing on a class of codes achieving the Singleton bound, we show that the lowest delay to recover any individual symbol not only depends on the erasure burst patterns correctable by a code, but also on whether the source symbols are encoded causally or non-causally. We also describe a few practical linear code constructions that achieve the performance limit discussed.