Explicit Rate-Optimal Streaming Codes with Smaller Field Size

TL;DR

This paper introduces an explicit rate-optimal streaming code construction that operates over a smaller field size of $q^2$ for all parameters, improving implementation efficiency while maintaining optimality.

Contribution

The authors provide the first explicit rate-optimal streaming code for all parameters over a minimal field size of $q^2$, reducing complexity compared to previous constructions.

Findings

Achieves rate-optimality over field size $q^2$ for all parameters.

Extends explicit code constructions to cover all parameter sets.

Reduces field size requirements compared to prior explicit codes.

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