NDLI: Random Sparse Linear Systems Observed Via Arbitrary Channels: A Decoupling Principle

Content Provider	IEEE Xplore Digital Library
Author	Dongning Guo Chih-Chun Wang
Copyright Year	2007
Description	Author affiliation: Dept. of Electr. Eng. & Comput. Sci., Northwestern Univ., Evanston, IL (Dongning Guo)
Abstract	This paper studies the problem of estimating the vector input to a sparse linear transformation based on the observation of the output vector through a bank of arbitrary independent channels. The linear transformation is drawn randomly from an ensemble with mild regularity conditions. The central result is a decoupling principle in the large-system limit. That is, the optimal estimation of each individual symbol in the input vector is asymptotically equivalent to estimating the same symbol through a scalar additive Gaussian channel, where the aggregate effect of the interfering symbols is tantamount to a degradation in the signal-to-noise ratio. The degradation is determined from a recursive formula related to the score function of the conditional probability distribution of the noisy channel. A sufficient condition is provided for belief propagation (BP) to asymptotically produce the a posteriori probability distribution of each input symbol given the output. This paper extends the authors' previous decoupling result for Gaussian channels to arbitrary channels, which was based on an earlier work of Montanari and Tse. Moreover, a rigorous justification is provided for the generalization of some results obtained via statical physics methods.
Starting Page	946
Ending Page	950
File Size	374501
Page Count	5
File Format	PDF
ISBN	9781424413973
DOI	10.1109/ISIT.2007.4557346
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-06-24
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Linear systems Vectors Gaussian channels Degradation Probability distribution Aggregates Signal to noise ratio Sufficient conditions Belief propagation Physics
Content Type	Text
Resource Type	Article

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