Frame Synchronization Techniques for Non-Binary LDPC Codes over GF(q)

The problem of frame synchronization of non-binary Low-Density Parity-Check (LDPC) codes is considered in this paper. We propose two techniques of blind frame synchronization that are based on syndrome calculation over the Galois Field GF(q). While the first technique computes hard values of the syndrome, the second one deals with probabilities. Furthermore, we present in this paper a theoretical analysis on the proposed synchronization criteria. This analysis is validated by comparison to simulated results. Although non-binary LDPC codes have short lengths and their decoding is very effective even at low Signal-to-Noise Ratio (SNR), simulation results have shown that the proposed Non-Binary Soft Syndrome (NBSS) based synchronization algorithm is well adapted to such codes. The Frame Error Rate (FER) curves obtained after synchronization and decoding are very close to the perfect synchronization case.