A Quadratic Field-Size Rate-Optimal Streaming Code for Channels with Burst and Random Erasures

Abstract

We study the problem of designing error-correcting codes over channels with burst and random erasures, when a strict decoding delay constraint τ is in place. Badr et al. introduced a channel model wherein for any sliding-window of width w, at most one of the following erasures patterns are permissible; (i) a burst erasure of length ≤ b or (ii) a total of ≤ a random erasures. We present a rate-optimal code construction under this model, which covers all feasible channel and delay parameters. In contrast to existing rate-optimal code families which require a field-size at least as large as $O\left( {\binom {\tau} {a} } \right)$, our construction needs a field-size quadratic in the decoding delay constraint. For some parameters, the construction can be over linear field-size.