  We introduce a new protocol for a lossy data compression algorithm which is
based on constraint satisfaction gates. We show that the theoretical capacity
of algorithms built from standard parity-check gates converges exponentially
fast to the Shannon's bound when the number of variables seen by each gate
increases. We then generalize this approach by introducing random gates. They
have theoretical performances nearly as good as parity checks, but they offer
the great advantage that the encoding can be done in linear time using the
Survey Inspired Decimation algorithm, a powerful algorithm for constraint
satisfaction problems derived from statistical physics.
