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On the Capacity of Memoryless Rewritable Storage Channels

机译：无记忆可重写存储通道的容量

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A number of modern storage technologies, when written to, exhibit substantial variability in the outcome of a write action. It is possible to mitigate the effect of the write uncertainty through the use of a feedback loop that rewrites the memory whenever judged necessary, in effect reshaping the write noise. This scheme highlights a tradeoff between the storage capacity of the memory and the cost of writing to it, measured for example in the number of rewrites. We have developed the model of a rewritable channel to provide an explicit form for this tradeoff and study other performance characteristics of such memories. In this paper, we describe some initial results on the information-theoretic analysis of the rewritable channel. We first consider the problem of determining the capacity of this channel with input cost constraints, and obtain a variety of results from which we extract insights that we believe are of value to memory designers. Our results include an upper bound on capacity of the form $logleft(Gammakapparight)$ , where $Gamma$ is a constant that can be easily calculated from the channel's statistics and $kappa$ is an average cost parameter. We also provide a lower bound on capacity with a similar form. We analyze the particular case of uniform write noise in detail, obtaining a closed form expression for the capacity-cost tradeoff for all possible cost parameters. We explore this formula from the capacity per unit cost perspective and establish that in order to achieve optimal energy and memory-wear per bit, it is sometimes strictly better to take advantage of the rewriting capability as opposed to writing only once; this observation has significant practical implications. We also include a discussion of the relevance of our work to r- al emerging memory technologies.
机译：写入时，许多现代存储技术在写入操作的结果中表现出很大的可变性。有可能通过使用反馈环路来减轻写不确定性的影响，该反馈环路在判断为必要时会重写存储器，从而有效地重塑了写噪声。该方案突出了在存储器的存储容量和对其进行写入的成本之间的折衷，例如以重写次数来衡量。我们已经开发了一种可擦写通道的模型，可以为这种折衷提供明确的形式，并研究此类存储器的其他性能特征。在本文中，我们描述了有关可擦写通道的信息理论分析的一些初步结果。我们首先考虑在输入成本约束下确定此通道容量的问题，然后获得各种结果，从中提取我们认为对存储器设计者有价值的见解。我们的结果包括$ logleft（Gammakapparight）$形式的容量上限，其中$ Gamma $是一个常数，可以很容易地从渠道的统计信息中计算得出，而$ kappa $是平均成本参数。我们还以类似的形式提供了容量的下限。我们详细分析了均匀写入噪声的特殊情况，为所有可能的成本参数获得了容量成本折衷的封闭式表达式。我们从每单位成本的容量角度探讨此公式，并确定为了获得最佳的每位能量和内存损耗，有时最好利用重写功能，而不是只写入一次。这一发现具有重大的实际意义。我们还讨论了我们的工作与新兴内存技术的相关性。

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