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Iterative message passing algorithms on graphs, which are generalized from the well-known turbo decoding algorithm, have been studied intensively in recent years because they can provide near-optimal performance and significant complexity reduction. In this paper, we demonstrate that this technique can be applied to pseudorandom code acquisition problems as well. To do this, we represent good pseudonoise (PN) patterns using sparse graphical models, then apply the standard iterative message passing algorithms over these graphs to approximate maximum-likelihood synchronization. Simulation results show that the proposed algorithm achieves better performance than both serial and hybrid search strategies in that it works at low signal-to-noise ratios and is much faster. Compared with full parallel search, this approach typically provides significant complexity reduction.