Sample Complexity of the Boolean Multireference Alignment Problem

Amit Singer; Emmanuel Abbe; Joao Pereira

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Sample Complexity of the Boolean Multireference Alignment Problem

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arxiv 1701.07540 v2 pith:SD5FI4MM submitted 2017-01-26 cs.IT math.IT

Emmanuel Abbe , Joao Pereira , Amit Singer This is my paper · ORCID

classification cs.ITmath.IT

keywords signalbooleanalignmentdimensionsexpressionmultireferenceproblemautocorrelations

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The Boolean multireference alignment problem consists in recovering a Boolean signal from multiple shifted and noisy observations. In this paper we obtain an expression for the error exponent of the maximum A posteriori decoder. This expression is used to characterize the number of measurements needed for signal recovery in the low SNR regime, in terms of higher order autocorrelations of the signal. The characterization is explicit for various signal dimensions, such as prime and even dimensions.

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