On the Capacity of Memoryless Rewritable Storage Channels

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 log (Γκ), where Γ is a constant that can be easily calculated from the channel's statistics and κ 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 real emerging memory technologies.