Rate-Optimal Streaming Codes for Channels with Burst and Isolated Erasures

TL;DR

This paper introduces a new family of streaming codes that achieve the optimal data recovery rate for channels with burst and isolated erasures, improving reliability in streaming applications.

Contribution

The paper provides an explicit construction of rate-optimal streaming codes for channels with burst and isolated erasures, matching the previously known upper bounds for all parameters.

Findings

Achieves rate upper bound for all feasible parameters

Explicit code construction provided

Improves data recovery in streaming channels

Abstract

Recovery of data packets from packet erasures in a timely manner is critical for many streaming applications. An early paper by Martinian and Sundberg introduced a framework for streaming codes and designed rate-optimal codes that permit delay-constrained recovery from an erasure burst of length up to $B$. A recent work by Badr et al. extended this result and introduced a sliding-window channel model $\mathcal{C}(N,B,W)$. Under this model, in a sliding-window of width $W$, one of the following erasure patterns are possible (i) a burst of length at most $B$ or (ii) at most $N$ (possibly non-contiguous) arbitrary erasures. Badr et al. obtained a rate upper bound for streaming codes that can recover with a time delay $T$, from any erasure patterns permissible under the $\mathcal{C}(N,B,W)$ model. However, constructions matching the bound were absent, except for a few parameter sets. In this paper, we present an explicit family of codes that achieves the rate upper bound for all feasible parameters $N$, $B$, $W$ and $T$.