# An Explicit Construction of Optimal Streaming Codes for Channels with Burst and Arbitrary Erasures

## TL;DR

This paper introduces an explicit, systematic construction of optimal streaming codes capable of correcting burst and arbitrary erasures in channels, using MDS and MRD codes, with applications to channels with high erasure rates.

## Contribution

It provides a new explicit construction of optimal streaming codes for high-rate channels, generalizing previous methods and analyzing field size requirements.

## Key findings

- Achieves optimal error correction for burst and arbitrary erasures.
- Uses off-the-shelf MDS and MRD codes for construction.
- Generalizes previous constructions to tolerate more sparse erasures.

## Abstract

This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding window erasure model, with burst and arbitrary losses, introduced by Badr et al. . Recently, two independents works by Fong et al. and Krishnan and Kumar have identified optimal streaming codes within this framework. In this paper, we introduce streaming code when the rate of the code is at least 1/2. Our proposed construction is explicit and systematic, uses off-the-shelf maximum distance separable (MDS) codes and maximum rank distance (MRD) Gabidulin block codes as constituent codes and achieves the optimal error correction. It presents a natural generalization to the construction of Martinian and Sundberg to tolerate an arbitrary number of sparse erasures. The field size requirement which depends on the constituent MDS and MRD codes is also analyzed.

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Source: https://tomesphere.com/paper/1903.07434