## 2 Conventional Work  
### Reversible Audio Data Hiding  
Most conventional reversible audio data hiding methods hide information in the time domain [20; 21; 22; 23]. We surveyed reversible information-hiding methods in the time domain as follows. [PERSON] proposed a technique to hide data in sign bits [21]. [PERSON] et al. proposed a method to expand the residual between the predicted and original signals based on Linear Predictive Coding (LPC) [22]. [PERSON] [20] extended the algorithm from [PERSON] et al.'s work. [PERSON] proposed a method to hide data in phase information [23]. The LPC-based hiding method is an effective method with high capacity. However, the LPC-based method has several disadvantages for the tampering detection approach. The algorithm aims to expand the residual to reserve hiding space, which means multiplying the residual by two and adding embedded data to the results, since residual values are floating numbers expressing predictor coefficients for a certain length of data. For blind extraction, the predictor coefficients should be embedded as a part of the payload in the embedding phase. However, each frame generates floating residuals, which are difficult to embed into the original data. Therefore, the LPC-based method assumes that two parties at the sending and receiving sides share the residual signal beforehand, which means that the LPC-based algorithm cannot achieve blind embedding. Moreover, it is difficult or impossible to predict certain types of data with stable and invariable frequency, such as white noise. In this case, residuals cannot be expanded to reserve hiding space.  
Alternatively, another method based on the discrete cosine transform (DCT) supplies an alternative domain to hide information. In the image field, the integer DCT (intDCT) is popularly used to achieve reversible information hiding [24; 25; 26] to embed data by modifying those integer DCT coefficients with peak amplitudes in each coefficient, which permits high capacity by coefficient expanding. [PERSON] et al. [24] expanded DCT coefficients  
Figure 1: Flowchart of tampering detection using information hiding.  
with peak amplitude to achieve imperceptible hiding. [PERSON] and [PERSON] [25] selected DCT coefficients in high-frequency components, which are supposed to have lower amplitude, to achieve high image quality. Additionally, [PERSON] et al.'s scheme [26] uses the medium-frequency coefficients of DCT-transformed cover images to embed. Hiding data into higher DCT coefficients of images results in lower distortion, while hiding them in lower DCT coefficients promises better robustness.  
Even though hiding in DCT coefficients by expansion has been proposed in the image field, only a few works discuss hiding in expanded DCT coefficients of audio data. Since the media data are different, distortion of images depends on visual perception, while audio distortion depends on auditory perception. Therefore, research on hiding with coefficient expansion for audio data may be worthwhile. When embedding information in the low, mid, and high DCT coefficients, the impact on the stego data may differ for image and audio. Therefore, it would be beneficial to investigate which band of DCT coefficients should be used to achieve high sound quality in data hiding for audio data.  
The work in [27] embeds data based on a replacement algorithm, which is not reversible but explores good hiding performance with high capacity by hiding data in the modified DCT domain of audio data. The work in [28] is based on traditional MDCT, which has half of the window overlap between adjacent frames and is inappropriate for tampering detection, since the overlapped windows result in false detection but have a good hiding capacity.