## 2 Related Works  
In this section, we recall some previous related works on audio watermarking algorithms. Over the past decades, many audio watermarking algorithms have appeared. Audio watermarking technology can be generally implemented in either the time domain [16; 17; 18] or transform domains. [PERSON] [16] proposed an audio algorithm by modifying the group amplitude. This algorithm had low payload capacity because it utilized three fragments to present a one-bit watermark. [PERSON] [17] presented an audio watermarking method with less robustness based on the time spread echo. [PERSON] [18] presented an audio watermarking algorithm for copyright protection by modifying the amplitude of each audio sample. In general, the time-domain algorithms can be implemented easily and require less computation, but are usually less robust to many kinds of digital signal processing attacks [12]. Compared with the time-domain algorithms, transform-domain algorithms are more robust because they take advantage of the audio signal characteristics and human auditory properties [19]. There are many transform domain algorithms, such as discrete Fourier transform (DFT) [20; 21; 22], DCT [6; 23], DWT [8; 19; 24; 25; 26; 27; 28] and singular value decomposition (SVD) [29]. [PERSON] [30] compared the characteristics of DFT, DCT and DWT when they were applied to watermarking algorithm. [PERSON] [20] presented a patchwork-based watermarking algorithm for stereo audio signals by exploiting the similarity of the two audio channels of stereo signals in the DFT domain. This algorithm had good robustness against several conventional attacks, but the payload capacity was not high. [PERSON] [21] presented a blind watermarking algorithm for audio signal to resist against self-synchronization by using fast Fourier transform. The algorithm embedded synchronization signals in the time domain and watermarks in the frequency domain. However, the self-synchronization code in time domain was vulnerable to some attacks, which would lead to the watermark being unable to survive. [PERSON] [22] proposed a digital audio watermarking algorithm which modified the middle frequency-band of DCT coefficients to embed the watermarks. [PERSON] [6] designed another patchwork-based audio watermarking method which embedded and extracted watermark bits in a multilayer framework by modifying the mean values of selected fragments in the DCT domain. The payload capacity was higher than that in paper [20]. [PERSON] [23] presented a large capacity audio watermarking algorithm by developing perceptual masking in the DCT domain. The authors claimed that the payload capacity of their algorithm reached 848.08 bps because they embedded the watermarks into three DCT coefficients respectively. However, they did not verify the overall performance of the algorithm when embedding the watermarks into those three DCT coefficients simultaneously. Due to the multi-resolution characteristics of DWT, many audio watermarking algorithms used DWT to analyze the frequency components of the audio signal in order to improve the performance of the algorithm. A variable-dimensional vector modulation (VDVM) algorithm was presented in paper [8], this algorithm maximized the efficiency of the norm-space DWT-based audio watermarking algorithm to achieve higher payload capacity, but its robustness was not very satisfactory. [PERSON] [19] used a genetic algorithm to search the optimal quantization step in order to improve both audio quality and robustness. This approach achieved good robustness against most of the attacks except for low-pass filtering, but its payload capacity was very low. [PERSON] [24] proposed a content-dependent localized audio watermarking algorithm to combat random cropping and time-scale modification. The watermark bits were embedded into the steady high-energy local regions to improve the robustness. This algorithm could resist synchronization attacks, but it had poor robustness against conventional signal processing attacks, such as equalization, re-sample and echo.