Coding for white-efficient memory
R. Ahlswede,Z. Zhang +1 more
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TLDR
This is the most basic quantity (the storage capacity) of a WEM ( X n, ϕn)n = 1∞ and a characterization of this and related quantities is given.Abstract:
We introduce write-efficient memories (WEM) as a new model for storing and updating information on a rewritable medium. There is a cost ϕ: X × X → R ∞ assigned to changes of letters. A collection of subsets C = {Ci: 1 ≤ i ≤ M} of X n is an (n, M, D) WEM code, if C i ∩ C j = ⊘ for all i ≠ j and if D max = max l⩽i,j⩽Mx n ϵC j Y n ϵC 1 max min ∑ j=1 n ϕ(x t , y t )⩽D . Dmax is called the maximal correction cost with respect to the given cost function. The performance of a code C can also be measured by two parameters, namely, the maximal cost per letter d C = n−1Dmax and the rate of the size r C = n−1 log M. The rate achievable with a maximal per letter cost d is thus R(d)= sup c:d c ⩽d r c . This is the most basic quantity (the storage capacity) of a WEM ( X n, ϕn)n = 1∞. We give a characterization of this and related quantities.read more
Citations
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TL;DR: It is interesting to note that the deterministic WEM behaves like the discrete noiseless channels of Shannon (1948), and some interesting properties for the maximization problem of information functions with multiple variables which are difficult to obtain otherwise are obtained.
References
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Journal ArticleDOI
Writing on dirty paper (Corresp.)
TL;DR: It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it, which is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N.
Journal ArticleDOI
On the capacity of computer memory with defects
C.D. Heegard,Abbas El Gamal +1 more
TL;DR: A computer memory with defects is modeled as a discrete memoryless channel with states that are statistically determined, and Arimoto-Blahut type algorithms are used to compute the storage capacity.
Journal ArticleDOI
How to reuse a “write-once≓ memory*
Ronald L. Rivest,Adi Shamir +1 more
TL;DR: It is demonstrated that such “write-once memories” can be “rewritten to a surprising degree” and an n-wit WOM is shown to have a “capacity” of up to n · log(n) bits.
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