Information Storage in the Stochastic Ising Model at Low Temperature
2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)(2019)
摘要
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) √n × √n grid. The measure of interest is the information capacity I
n
(t) =△ max
pX0
I(X
0
; X
t
), where the initial spin configuration X
0
is a user-controlled input and the output configuration X
t
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 X
0
is drawn according to the Gibbs measure, then I(X
0
; X
t
) ≤ 1 + o(1) for t ≥ exp (cn
1/4+ε
). On the other hand, when scaling time with β, we propose a stripe-based coding scheme that stores order of √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 I
n
(t) for β > 0.
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关键词
Gibbs measure,scaling time,survival time,striped-based storage scheme,initial steps,information storage,stochastic Ising model,data stabilization,magnetic storage technologies,interacting particle systems,information capacity,initial spin configuration X,user-controlled input,output configuration X,Glauber dynamics,zero-temperature regime,single bit,exponential time
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