Lattice Erasure Codes of Low Rank with Noise Margins

TL;DR

This paper introduces low rank lattice erasure codes that extend MDS codes by optimizing noise margins under erasures and power constraints, with derived performance bounds and specific code designs.

Contribution

It generalizes MDS codes to low rank lattice codes with noise margin optimization for erasure channels, providing bounds and design methods.

Findings

Derived performance bounds for low rank lattice codes.

Presented specific code designs meeting noise margin and power constraints.

Demonstrated improved robustness over traditional MDS codes.

Abstract

We consider the following generalization of an $(n,k)$ MDS code for application to an erasure channel with additive noise. Like an MDS code, our code is required to be decodable from any $k$ received symbols, in the absence of noise. In addition, we require that the noise margin for every allowable erasure pattern be as large as possible and that the code satisfy a power constraint. In this paper we derive performance bounds and present a few designs for low rank lattice codes for an additive noise channel with erasures.