The Belief in TAP

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Yoshiyuki Kabashima, David Saad


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 J{ bits selected randomly from the original message. We examine the efficacy of solutions obtained by the two methods for various values of J{ and show that solutions for J{ 2': 3 may be sensitive to the choice of initial conditions in the case of unbiased patterns. Good approximations are obtained generally for J{ = 2 and for biased patterns in the case of J{ 2': 3, especially when Nishimori's temperature is being used.