Belief propagation vs. TAP for decoding corrupted messages

¹ Department of Computational Intelligence and Systems Science Tokyo Institute of Technology - Yokohama 2268502, Japan
² The Neural Computing Research Group, Aston University Birmingham B4 7ET, UK

Received: 5 February 1998
Accepted: 7 October 1998

Abstract

We employ two different methods, based on belief propagation and TAP, for decoding corrupted messages encoded by employing Sourlas's method, where the code word comprises products of K bits selected randomly from the original message. We show that the equations obtained by the two approaches are similar and provide the same solution as the one obtained by the replica approach in some cases (K=2). However, we also show that for and unbiased messages the iterative solution is sensitive to the initial conditions and is likely to provide erroneous solutions; and that it is generally beneficial to use Nishimori's temperature, especially in the case of biased messages.