Abstract
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.
Highlights
Pulse-position modulation (PPM), a technique that achieves very good average-power efficiency, is widely used in multiple types of communications [1]–[5]
As the order of modulation increases, for example, if we extend our method from 4-Differential pulse-position modulation (DPPM) to 8-DPPM, the proposed method based on the equivalent source and channel models [27] will become much more complex, because the equivalent source symbols become much more
The chip flipping rates over the general IDS channel are caused by the additive white Gaussian noise (AWGN) channel and DPPM symbol-by-symbol soft-decision detection, resulting in symbol insertions/deletions and substitutions that can be measured by the Levenshtein distance [30]
Summary
Pulse-position modulation (PPM), a technique that achieves very good average-power efficiency, is widely used in multiple types of communications [1]–[5]. To deal with the insertion, deletion and substitution errors caused by chip flipping with symbol-by-symbol DPPM detection, based on the equivalent source and channel models, an efficient decoding scheme using hidden Markov model (HMM) is proposed. With the known watermark sequence w and the received symbol sequence r, a hard-decision forward-backward decoding algorithm based on the HMM is used to correct symbol insertion and deletion errors, and to output the estimate of the codeword v. PROPOSED IMPROVED DECODING SCHEME In order to correct the symbol insertions, deletions and substitutions caused by the general IDS channel, based on the equivalent source and channel models, we propose an efficient decoding scheme which consists of inner decoding and outer decoding. Compared with the decoding scheme using the DP and the Viterbi algorithm as inner decoding algorithms [27], [29], the proposed decoding scheme has superior performance in correcting insertion, deletion and substitution errors in DPPM transmission
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