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Abstract:
We show the similarity between belief propagation and TAP,
for decoding corrupted messages encoded by Sourlas's method. The
latter is a special case of the Gallager error-correcting code,
where the code word comprises products of bits selected randomly
from the original message. We examine the efficacy of solutions
obtained by the two methods for various values of and show that
solutions for may be sensitive to the choice of initial conditions
in the case of unbiased patterns. Good approximations are obtained
generally for and for biased patterns in the case of , especially
when Nishimori's temperature is being used.
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