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Differential pulse-position modulation (DPPM) shows significant power and bandwidth efficiency, but suffers from serious insertion/deletion and substitution errors if the DPPM soft-decision symbol-by-symbol detection method is used. In this paper, based on the DPPM transmission scheme combining the watermark with the low-density parity-check (LDPC) code, and the equivalent source and channel models, we propose an efficient decoding scheme using hidden Markov model (HMM). Specifically, with the known watermark and the equivalent source and channel models, a hidden markov model is first established to estimate the insertion/deletion errors of the received symbols. Then, a hard-decision forward-backward algorithm is used to recover synchronization and output the estimate of the codeword. Finally, Belief-Propagation (BP) decoding algorithm in the logarithmic domain is performed to correct the residual substitution errors. Simulation results reveal that compared with the decoding scheme using the dynamic programming (DP) and Viterbi algorithms, the proposed decoding scheme has superior performance in correcting insertion, deletion and substitution errors in DPPM transmission.

Correcting Insertions/Deletions in DPPM Using Hidden Markov Model