Abstract
The Davey–MacKay (DM) concatenated code employing the symbol-level watermark decoding algorithm is able to correct a large number of binary insertions, deletions, and substitutions, while it has the high computational complexity for recovering the synchronization. In the DM concatenated scheme, at the large insertion/deletion probability, in order to achieve the reliable output, the watermark decoder needs to perform the forward and backward passes on a very large trellis. In this paper, a threshold is selected to prevent the paths having very low forward and backward quantities from participating in the calculation of log-likelihood ratios from the watermark decoder. Simulation results show that great reduction in the complexity of the decoding algorithm is achieved at a very slight expense of accuracy.
Highlights
Insertions and deletions, which could induce the loss of synchronization, occur in many practical systems such as the imperfect synchronization in the communication systems [1], the file updates under general edits [2], [3], the bitpatterned media recording channel [4], [5], the multimedia watermarking methods in speech watermarking [6], and the differential pulse position modulation system [7]
Liu: On the Concatenated Transmission Scheme With the Low-Complexity Symbol-Level Watermark Decoder states for the one symbol in the non-binary low-density parity-check (NB-LDPC) code, where X is the number of states at each time in the trellis
NB-LDPC code (NL, KL ) over GF(q): NL denotes the number of symbols in a codeword, KL is the number of information symbols
Summary
Insertions and deletions, which could induce the loss of synchronization, occur in many practical systems such as the imperfect synchronization in the communication systems [1], the file updates under general edits [2], [3], the bitpatterned media recording channel [4], [5], the multimedia watermarking methods in speech watermarking [6], and the differential pulse position modulation system [7]. Once insertions or deletions exist in the received sequences, symbol and block boundaries are unknown [8]–[11]. The Davey-MacKay (DM) concatenated code was proposed to correct multiple binary insertions and deletions, and regarded as the most promising approach [15]. In this scheme, the watermark and non-binary low-density parity-check (NB-LDPC) codes were employed as inner and outer codes respectively. Y. Liu: On the Concatenated Transmission Scheme With the Low-Complexity Symbol-Level Watermark Decoder states for the one symbol in the NB-LDPC code, where X is the number of states at each time in the trellis.
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