Explicit Rate-Optimal Streaming Codes with Smaller Field Size

Streaming codes are a class of packet-level erasure codes that ensure packet recovery over a sliding window channel which allows either a burst erasure of size $b$ or $a$ random erasures within any window of size $(tau+1)$ time units, under a strict decoding-delay constraint $tau$. The field size over which streaming codes are constructed is an important factor determining the complexity of implementation. The best known explicit rate-optimal streaming code requires a field size of $q^2$ where $q ge tau+b-a$ is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible ${a,b,tau}$ parameters, over a field of size $q^2$ for prime power $q ge tau$. This is the smallest-known field size of a general explicit rate-optimal construction that covers all ${a,b,tau}$ parameter sets. We achieve this by modifying the non-explicit code construction due to Krishnan et al. to make it explicit, without change in field size.