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 in determining the implementation complexity. The best-known explicit rate-optimal streaming code, which covers all
$\{a,b,\tau \}$
parameter choices, 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 over a field of size
$q^{2}$
, for prime power
$q \ge \tau $
. This is the smallest known field size for an explicit rate-optimal construction that takes into account all
$\{a,b,\tau \}$
parameters. We achieve this by modifying the non-explicit code construction due to Krishnan et al., without changing the field size. We also present a generalization of our construction, which results in streaming codes over further smaller fields by trading off code rate.