An Explicit Rate-Optimal Streaming Code for Channels with Burst and Arbitrary Erasures

TL;DR

This paper presents an explicit, rate-optimal streaming code for channels with burst and arbitrary erasures, achieving capacity with a quadratic field size, improving on previous constructions.

Contribution

It introduces a new explicit coding scheme that attains the channel capacity with a field size scaling quadratically with delay, unlike prior methods.

Findings

Achieves channel capacity with explicit codes

Uses quadratic field size relative to delay

Applicable to channels with burst and arbitrary erasures

Abstract

This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While the capacity of a channel that introduces only bursts of erasures is well known, only recently, the capacity of a channel with either one burst of erasures or multiple arbitrary erasures in any fixed-sized sliding window has been established. However, the codes shown to achieve this capacity are either non-explicit constructions (proven to exist) or explicit constructions that require large field size that scales exponentially with the delay. This work describes an explicit rate-optimal construction for admissible channel and delay parameters over a field size that scales only quadratically with the delay.