  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.
