Blind Frame Synchronization of Product Codes Based on the Adaptation of the Parity Check Matrix

We present in this paper a blind frame synchronization method based on the adaptation of the parity check matrix of the code. The blind synchronizer is initially based on the calculation of the Log-Likelihood Ratios (LLR) of the syndrome elements, obtained using the parity check matrix of the code. Before applying our synchronization procedure, we propose in this paper to rearrange the parity check matrix of the code according to the reliability of the received symbols as previously introduced for decoding linear block codes with high density parity check matrix. Simulation results show that the Frame Error Rate (FER) curves obtained after applying the proposed synchronization method to product codes are very close to the ones with perfect synchronization. In addition to its powerful synchronization properties, the main advantage of the proposed synchronization algorithm is its capability of being introduced as a part of the decoder so that no additional material is required for the synchronization step.