Near-Optimal Codes for Information Embedding in Gray-Scale Signals

High-performance steganography requires large embedding rate and small distortion, i.e., high embedding efficiency. Steganographic codes (stego-codes) derived from covering codes can improve embedding efficiency. In this paper, a new method is proposed to construct binary stego-codes for LSB embedding in gray-scale signals, which shows that not just one but a family of stego-codes can be generated from a covering code by combining Hamming codes and wet paper codes. This method can greatly expand the set of embedding schemes as applied to steganography. Performances of stego-code families (SCF) of structured codes and random codes are analyzed. SCFs of random codes can approach the rate-distortion bound on LSB embedding for any chosen embedding rate. Furthermore, SCFs are modified for applications in ±1 embedding, and a treble layered embedding method for ±2 embedding is obtained. By combining the modified SCFs and the treble layered method, a near-optimal scheme for ±2 embedding is presented.