## 1 Introduction  
In the era of fifth generation (5G) mobile networks, information security draws much more attention than ever and various data hiding schemes and secure communication techniques have been proposed [1, 2, 3, 4]. The data hiding technique embeds secret messages into a carrier, such as an audio, a video, or a digital image. Upon receiving the marked carrier, the receiver extracts the secret data and recovers the carrier. Among the existing data hiding methods, not all of them can losslessly recover the carrier. A method that can perfectly recover a carrier is classified as a reversible data hiding (RDH) method [5, 6, 7, 8]; otherwise, it is irreversible [9, 10, 11, 12]. The most popular carrier is digital images. Since there are various compression formats for digital images, including lossy compression [13, 14, 15] and lossless compression [16, 17], an efficient data hiding techniques should be designed according to the features of the target format. In this research, we focus on the data embedding of VQ compressed images. Before VQ compression, a codebook should be established first. The LBG (Lindo-Buzo-Gray) algorithm [18] is a commonly applied technique to train a codebook. The compression process starts with partitioning the given image into disjoint blocks. Then, each block is encoded by finding its best fitting codeword in the codebook and represent the block with the index of the found codeword. As a result, the given image is encoded into an index table, which is also called the VQ compressed code. Some methods have been proposed to further compress the VQ code [16, 19]. In 1992, [PERSON] proposed side-match vector quantization (SMVQ) [19]. Only the first row and the first column of the index table are recorded. In the decompression phase, blocks of the first row and the first column are decompressed first. Then, the remaining image blocks are predicted by side-matching with the codewords in the codebook. The compress ratio is very high. However, the quality of the decompressed image is poor. In 2004, [PERSON] et al. proposed a reversible scheme [20] to embed secret data in SOC-encoded VQ indices. The indicator bit of each SOC-encoded index is directly replaced by a secret bit. When a flip of indicator bit is encountered, its following format of index code should be exchanged correspondingly. The embedding rate is satisfactory; however, exchange of index format severely expands the code length. After that, improved versions [21; 22; 23] were proposed. In the original version of SOC data hiding, to switch an uncompressible code into a camouflaged compressed code, a reserved code is applied followed by the original index. Which makes a great expansion of file size and reduces the ability of SOC compression. In 2011, [PERSON] et al. proposed an improved version [21], which leaves the uncompressible index unembedded and thus releases the reserved code. In 2016, [PERSON] and [PERSON] proposed a data hiding scheme [23] based on the improved search-order coded (ISOC) VQ indices. The compression ability and the embedding capacity can be further improved. These studies make different trade-offs between embedding rate and file expansion based on the same scheme of indicator bit replacement. In recent years, RDH for VQ index table based on different kinds of compression methods for VQ have been proposed [24; 25; 26; 27]. Another series of RDH for VQ index table is to apply the de-clustering concept, which is proposed by [PERSON] et al. at 2006 [28]. With the help of SMVQ, indices of VQ can switch between a dissimilar pair to embed a secret bit without expanding the code length. Later, different kinds of clustering techniques [29; 30] have been proposed to improve the hiding capacity of the de-clustering approach. In this paper, we incorporate the de-clustering technique with an SOC-based method to improve data hiding capacity and information security. A two-layer RDH scheme for VQ index table is proposed. The de-clustering concept is applied to embed the first layer of secret data.