Explicit Rate-Optimal Streaming Codes with Smaller Field Size

Abstract

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 (τ+1) time units, under a strict decoding-delay constraint τ. 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 q2 where q≥τ+b−a is a prime power. In this work, we present an explicit rate-optimal streaming code, for all possible {a,b,τ} parameters, over a field of size q2 for prime power q≥τ. This is the smallest-known field size of a general explicit rate-optimal construction that covers all {a,b,τ} 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.