  The surge in mobile broadband data demands is expected to surpass the
available spectrum capacity below 6 GHz. This expectation has prompted the
exploration of millimeter wave (mm-wave) frequency bands as a candidate
technology for next generation wireless networks. However, numerous challenges
to deploying mm-wave communication systems, including channel estimation, need
to be met before practical deployments are possible. This work addresses the
mm-wave channel estimation problem and treats it as a beam discovery problem in
which locating beams with strong path reflectors is analogous to locating
errors in linear block codes. We show that a significantly small number of
measurements (compared to the original dimensions of the channel matrix) is
sufficient to reliably estimate the channel. We also show that this can be
achieved using a simple and energy-efficient transceiver architecture.
