Lattice Erasure Codes of Low Rank with Noise Margins

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. Index terms Lattices, Erasure Codes, MDS Codes, Compound Channel.