Analytical Performance Evaluation of Frame Synchronization for Data with Known, Unequal Distribution over Binary Symmetric Channel

In a prior work, we derived the LLRTD metric for frame synchronization over a binary symmetric channel (BSC), where data frames are of unknown and unequal lengths and with synchronization words aperiodically inserted, data symbols have a known, unequal distribution. The performance of the metric was evaluated using simulations. Here we provide an analytical performance evaluation for the LLRTD metric. For the purpose of comparison, we also provide an analytical performance evaluation for the hard correlation (HC) metric in the case where the data has a known, unequal distribution. The results obtained for both metrics are found to be in line with the simulation results earlier obtained and confirm that the LLRTD outperforms the HC metric in all cases considered.