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RSB Decoupling Property of MAP Estimators
The large-system decoupling property of a MAP estimator is studied when it
estimates the i.i.d. vector from the observation
with
being chosen from a wide range of matrix ensembles, and the noise vector
being i.i.d. and Gaussian. Using the replica method, we show
that the marginal joint distribution of any two corresponding input and output
symbols converges to a deterministic distribution which describes the
input-output distribution of a single user system followed by a MAP estimator.
Under the RSB assumption, the single user system is a scalar channel with
additive noise where the noise term is given by the sum of an independent
Gaussian random variable and correlated interference terms. As the RSB
assumption reduces to RS, the interference terms vanish which results in the
formerly studied RS decoupling principle.Comment: 5 pages, presented in Information Theory Workshop 201
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