Iterative decoding of the reverse concatenated watermark code for correcting synchronization errors

A new iterative decoding scheme was introduced for the reverse concatenated watermark code to improve the decoding performance in the presence of insertions, deletions and substitutions. The scheme fed back the hard-decision estimations into the inner decoder of the reverse concatenated watermark code and the new reference sequence chose the modulo-2 sum of the original watermark and the codeword with the hard decisions, reducing the impact of the codeword to the watermark sequence and improving the reference information of the inner decoder. The forward-backward algorithm used the new reference sequence and the updated effective substitution error probability to refine the output probability and then to update the forward and backward quantities, which improved the reliability of the likelihood for each bit in the inner decoder and enhanced the overall performance. It is shown that the overall performance improves when using the hard-decision iterative scheme to the reverse concatenated watermark codes.