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Summary: Message-Passing Algorithms and Improved LP Decoding
Sanjeev Arora
Princeton Universtiy
Constantinos Daskalakis
CSAIL, MIT
David Steurer
Princeton University
ABSTRACT
Linear programming decoding for low-density parity check
codes (and related domains such as compressed sensing) has
received increased attention over recent years because of its
practical performance --coming close to that of iterative de-
coding algorithms-- and its amenability to finite-blocklength
analysis. Several works starting with the work of Feldman
et al. showed how to analyze LP decoding using properties
of expander graphs. This line of analysis works for only low
error rates, about a couple of orders of magnitude lower than
the empirically observed performance. It is possible to do
better for the case of random noise, as shown by Daskalakis
et al. and Koetter and Vontobel.
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