基于负载均衡理论的闪存调制编码
Modulation Codes for Flash Memory Based on Load-Balancing Theory
摘要：
在本文中，我们考虑的调制码的实际多级闪存存储系统的单元级。我们不是最大化设备的寿命[Ajiang-isit 07 -01，Ajiang-isit 07 -02，Yaakobi_verdy_siegel_aller_allerton 08，Finucane_Liu_Mitzenmacher_aller08]，而是最大化每个单元级别存储的平均信息量，这被定义为存储效率。使用这个框架，我们表明，最坏情况下的标准[Ajiang-isit 07 -01，Ajiang-isit 07 -02，Yaakobi_verdy_siegel_aller_allerton 08]和平均情况下的标准[Finucane_Liu_Mitzenmacher_aller08]是我们的目标函数的两个极端情况。提出了一种自随机调制码，它是渐近最优的，对于任意的输入字母表和独立同分布。投入分配在实际的闪存系统中，单元级的数量仅是适度大的。所以渐近性能可能不能说明全部情况。利用负载均衡理论的工具，分析了自随机调制码的存储效率。结果表明，只有一小部分的细胞被利用时，细胞级的数量只有适度的大。我们还提出了一个负载均衡调制码，基于被称为“两个随机选择的权力”[Mitzenmacher 96 thepower]的现象，以提高实际系统的存储效率。理论分析和仿真结果表明，我们的负载均衡调制码可以提供显着的增益，实际的闪存存储系统。虽然是伪随机的，我们的方法实现了相同的负载均衡性能，对于i.i.d.输入，作为基于两个随机选择的幂的纯随机方法。
英文摘要：
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.
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