Explicit Rate-Optimal Streaming Codes With Smaller Field Size
Myna Vajha, Vinayak Ramkumar, M. Nikhil Krishnan, P. Vijay Kumar · IEEE Transactions on Information Theory · 2023
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.