# Construction of Fixed Rate Non-Binary WOM Codes based on Integer Programming

## TL;DR

This paper introduces a systematic construction method for fixed rate non-binary WOM codes using integer programming, enabling efficient multi-write capabilities and interference reduction in flash memory storage.

## Contribution

It presents a novel construction approach for non-binary WOM codes with systematic encoding and labeling methods based on integer programming, improving write endurance and flexibility.

## Key findings

- Achieves the known upper bound on the number of writes in many cases.
- Constructs WOM codes that reduce inter cell interference in flash memories.
- Demonstrates flexibility across various storage configurations.

## Abstract

In this paper, we propose a construction of non-binary WOM (Write-Once-Memory) codes for WOM storages such as flash memories. The WOM codes discussed in this paper are fixed rate WOM codes where messages in a fixed alphabet of size $M$ can be sequentially written in the WOM storage at least $t^*$-times. In this paper, a WOM storage is modeled by a state transition graph. The proposed construction has the following two features. First, it includes a systematic method to determine the encoding regions in the state transition graph. Second, the proposed construction includes a labeling method for states by using integer programming. Several novel WOM codes for $q$ level flash memories with 2 cells are constructed by the proposed construction. They achieve the worst numbers of writes $t^*$ that meet the known upper bound in many cases. In addition, we constructed fixed rate non-binary WOM codes with the capability to reduce ICI (inter cell interference) of flash cells. One of the advantages of the proposed construction is its flexibility. It can be applied to various storage devices, to various dimensions (i.e, number of cells), and various kind of additional constraints.