Theoretical analysis of a MAP based blind frame synchronizer

We have recently proposed in a blind frame synchronization method based on a maximum a posteriori (MAP) approach. In this letter, we study the properties of this method and show that this synchronization technique is well suitable for codes having a sparse parity check matrix, such as low-density parity-check (LDPC) codes. We also find the probability distributions involved in our synchronization criterion and expand the analytical expression of the probability of false synchronization. Through computer simulations we validate our theoretical results and show that this synchronization technique has excellent performance when applied to LDPC codes. We also show that this method outperforms another approach of blind frame synchronization that computes hard values of the syndrome instead of its log-likelihood ratios (LLR).