Modulation Codes for Flash Memory Based on Load-Balancing Theory

TL;DR

This paper introduces load-balancing based modulation codes for multilevel flash memory, optimizing storage efficiency by balancing cell usage, and demonstrates their effectiveness through theoretical analysis and simulations.

Contribution

It proposes a load-balancing modulation code that improves storage efficiency in practical flash memory systems, extending existing criteria with a novel approach.

Findings

Self-randomized modulation code is asymptotically optimal for i.i.d. inputs.

Load-balancing modulation code significantly improves storage efficiency.

Performance of the proposed code matches that of the ideal random approach.

Abstract

In this paper, we consider modulation codes for practical multilevel flash memory storage systems with cell levels. Instead of maximizing the lifetime of the device [Ajiang-isit07-01, Ajiang-isit07-02, Yaakobi_verdy_siegel_wolf_allerton08, Finucane_Liu_Mitzenmacher_aller08], we maximize the average amount of information stored per cell-level, which is defined as storage efficiency. Using this framework, we show that the worst-case criterion [Ajiang-isit07-01, Ajiang-isit07-02, Yaakobi_verdy_siegel_wolf_allerton08] and the average-case criterion [Finucane_Liu_Mitzenmacher_aller08] are two extreme cases of our objective function. A self-randomized modulation code is proposed which is asymptotically optimal, as, for an arbitrary input alphabet and i.i.d. input distribution. In practical flash memory systems, the number of cell-levels is only moderately large. So the asymptotic performance as may not tell the whole story. Using the tools from load-balancing theory, we analyze the storage efficiency of the self-randomized modulation code. The result shows that only a fraction of the cells are utilized when the number of cell-levels is only moderately large. We also propose a load-balancing modulation code, based on a phenomenon known as "the power of two random choices" [Mitzenmacher96thepower], to improve the storage efficiency of practical systems. Theoretical analysis and simulation results show that our load-balancing modulation codes can provide significant gain to practical flash memory storage systems. Though pseudo-random, our approach achieves the same load-balancing performance, for i.i.d. inputs, as a purely random approach based on the power of two random choices.