Reliable Robust Adaptive Steganographic Coding Based on Nested Polar Codes

Steganography is the art of covert communication that pursues the secrecy of concealment. In adaptive steganography, the most commonly used framework of steganography, the sender embeds a “secret message” signal within another “cover” signal with respect to a certain adaptive distortion function that measures the distortion incurred, contributing to the composite “stego” signal that resembles the cover, and the receiver extracts the “secret message” signal from the stego. When the communication channel between the sender and the receiver is noisy, robust steganography is needed, in which robust adaptive steganographic coding plays a central role. The existing robust adaptive steganographic coding methods can only provide very limited robustness, and they fail when the communication channel is bad. To ensure the success of covert communication, we propose a reliable robust adaptive steganographic coding scheme based on nested polar codes that possesses the highest robustness among the existing algorithms while the security performance is also maintained. Theoretically, we show that for the most important binary embedding, in the special case where the communication channel is a Binary Symmetric Channel (BSC), the proposed scheme is optimal under the constant distortion profile as the cover length $N$ tends to infinity through powers of two when the design embedding rate is large enough. Experimentally, our method is capable of making sure the perfect extraction of the secret message in situations where the embedding rate is large or the communication channel is bad, while the existing algorithms are not applicable in these scenarios.