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 <tex>$b$</tex> or <tex>$a$</tex> random erasures within any window of size (<tex>$\tau+1$</tex>) time units, under a strict decoding-delay constraint <tex>$\tau$</tex>. 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 <tex>$q^{2}$</tex> where <tex>$q\geq\tau+b-a$</tex> is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible <tex>$\{a, b,\tau\}$</tex> parameters, over a field of size <tex>$q^{2}$</tex> for prime power <tex>$q\geq \tau$</tex>. This is the smallest-known field size of a general explicit rate-optimal construction that covers all <tex>$\{a, b, \tau\}$</tex> 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.

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