Rapid Acquisition of Gold Codes and Related Sequences Using Iterative Message Passing on Redundant Graphical Models

A recent study, [1], demonstrated that iterative message passing algorithms (iMPAs) can be applied to rapidly acquire pseudo-noise (PN) sequences with low-complexity. Furthermore, a second work, [2], showed that significant benefits can be obtained using redundant graphical models, in case of linear feedback shift register (LFSR) sequences with sparse generator polynomials. Starting from these results, we address the problem of fast detection to Gold codes and LFSR sequences with dense generators. We will prove that these two aspects are closely related, and that, constructing redundant Tanner Graphs (TGs) from sparse higher-degree generator polynomials, it is possible to rapidly acquire these PN sequences at low signal-to-noise ratio (SNR), and with a low complexity. We also propose another distinct approach for acquiring Gold sequences using iterative methods based on a hierarchical model for the two LFSR generators that comprise a Gold code.