Rewritable Codes for Flash Memories Based Upon Lattices, and an Example Using the E8 Lattice

TL;DR

This paper introduces a lattice-based rewriting code for flash memories that allows multiple data writes without decreasing cell values, using the E8 lattice as a concrete example with numerical results.

Contribution

It presents a novel lattice-based coding scheme for flash memories enabling multiple writes without cell value reduction, including an explicit example with the E8 lattice.

Findings

Rewriting code construction partitions memory space into blocks.

Minimum number of writes is linear in code parameters.

Numerical results demonstrate the effectiveness of the E8 lattice example.

Abstract

A rewriting code construction for flash memories based upon lattices is described. The values stored in flash cells correspond to lattice points. This construction encodes information to lattice points in such a way that data can be written to the memory multiple times without decreasing the cell values. The construction partitions the flash memory's cubic signal space into blocks. The minimum number of writes is shown to be linear in one of the code parameters. An example using the E8 lattice is given, with numerical results.