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 (+1) time units, under a strict decoding-delay constraint. 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, \ parameter choices, requires a field size of q^2, where q +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. This is the smallest known field size for an explicit rate-optimal construction that takes into account all \a, b, \ 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.