We study a new synchronization algorithm based on low-density parity check codes. The algorithm was developed for scenarios with redundant information in 2010, [1]. We describe a revised version of the algorithm and, for the first time, we discuss the fundamentals about the coding and decoding theory. The results of this analysis define the scope and restrictions of the algorithm. We show that the algorithm is capable of recovering synchronization even in scenarios without redundant information. The algorithm has the characteristic of using not only cyclically permutable codes like the related proposals. Nevertheless special attention must be paid to short codes. Finally, an accurate approximation of the bound is introduced by using maximum likelihood decoding.