# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1904.06212