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Designing Floating Codes for Expected Performance

机译：设计浮动代码以实现预期的性能

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摘要

Floating codes are codes designed to store multiple values in a Write Asymmetric Memory, with applications to flash memory. In this model, a memory consists of a block of n cells, with each cell in one of q states {0,1,...,q -1}. The cells are used to represent k variable values from an ¿-ary alphabet. Cells can move from lower values to higher values easily, but moving any cell from a higher value to a lower value requires first resetting the entire block to an all 0 state. Reset operations are to be avoided; generally a block can only experience a large but finite number of resets before wearing out entirely. A code here corresponds to a mapping from cell states to variable values, and a transition function that gives how to rewrite cell states when a variable is changed. Previous work has focused on developing codes that maximize the worst-case number of variable changes, or equivalently cell rewrites, that can be experienced before resetting. In this paper, we introduce the problem of maximizing the expected number of variable changes before resetting, given an underlying Markov chain that models variable changes. We demonstrate that codes designed for expected performance can differ substantially from optimal worst-case codes, and suggest constructions for some simple cases. We then study the related question of the performance of random codes, again focusing on the issue of expected behavior.
机译：浮动代码是旨在将多个值存储在写非对称存储器中的代码，并适用于闪存。在此模型中，存储器由n个单元的块组成，每个单元处于q状态{0,1，...，q -1}之一。单元格用于表示来自A字母的k个变量值。单元可以轻松地从较低的值移动到较高的值，但是将任何单元从较高的值移动到较低的值首先需要将整个块重置为全0状态。避免复位操作；通常，一个块只能在完全耗尽之前经历大量但有限的复位。这里的代码对应于从单元格状态到变量值的映射，以及一个转换函数，该转换函数给出了如何在更改变量时重写单元格状态。先前的工作集中在开发代码，以使重置之前可以经历的最坏情况的变量更改或等效的单元重写次数最大化。在本文中，我们介绍了在给定潜在的建模变量变化的马尔可夫链的前提下，在重置之前最大化变量变化的预期数量的问题。我们证明了为预期性能而设计的代码可能与最佳的最坏情况代码大不相同，并建议了一些简单情况的构造。然后，我们研究随机代码的性能的相关问题，再次关注预期行为的问题。

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