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
$q\geq\tau+b-a$
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
$q\geq \tau$
. 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.