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Information Storage in the Stochastic Ising Model at Low Temperature
Name
isit2019_storage_i.pdf
Description
Accepted version
Size
184.35 KB
Format
Adobe PDF
Checksum (MD5)
ba6b3512bf753bccf720dae9e021aa67
Author(s)
Goldfeld, Ziv
Bresler, Guy
Polyanskiy, Yury
Journal
IEEE International Symposium on Information Theory - Proceedings
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Author's final manuscript
Abstract
© 2019 IEEE. Motivated by questions of data stabilization in emerging magnetic storage technologies, we study the retention of information in interacting particle systems. The interactions between particles adhere to the stochastic Ising model (SIM) on the two-dimensional (2D) \sqrt n × \sqrt n grid. The measure of interest is the information capacity {I-n}\left(t\right) \triangleq {\max -{{p-{{X-0}}}}}I\left({{X-0};{X-t}}\right), where the initial spin configuration X0 is a user-controlled input and the output configuration Xt is produced by running t steps of Glauber dynamics. After the results on the zero-temperature regime reported last year, this work focuses on the positive but low temperature regime. We first show that storing more than a single bit for an exponential time is impossible when the initial configuration is drawn from the equilibrium distribution. Specifically, if X0 is drawn according to the Gibbs measure, then I(X0; Xt) ≤ 1 + o(1) for t \geq \exp \left({c{n^{\frac{1}{4} + \varepsilon }}}\right). On the other hand, when scaling time with β, we propose a stripe-based coding scheme that stores order of \sqrt n bits for exp(β) time. Key to the analysis of the scheme is a new result on the survival time of a single plus-labeled stripe in a sea of minuses. Together, the 1-bit upper bound and the striped-based storage scheme constitute initial steps towards a general analysis of In(t) for β > 0.
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/ISIT.2019.8849513
