Non-Binary Polar Codes for Steganography

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Abstract
Coding scheme is the fundamental part of steganography to embed message in cover data arousing as less distortion as possible. In some recent developed robust steganographic methods, it also undertakes error-correction on message extracted from stego data transmitted in lossy communication channel. This paper proposes Non-Binary Polar Codes (NBPCs) based stego codes which could directly implement multi-layered steganographic embedding without multi-layered decomposition. Moreover, we extend proposed scheme for robust steganography, which has the scalable ability of error-correcting and avoids the problem of allocating embedded redundant payload in multiple layers for error-correcting. By analyzing steganographic embedding and error-correcting for robust steganography, we find that both tasks are adequate to be solved in identical form of Maximum A Posteriori decoding (MAP decoding). Consequently, we develop successive cancellation list MAP decoding for NBPCs built on Galois Field. Besides, we propose a quick estimation method to directly estimate joint probabilities of modification on multi-layer bits to accelerate proposed coding scheme. Compared with existing coding schemes for steganography and robust steganography, such as double-layered STCs, SPCs and doublelayered dual-STCs, the experimental results demonstrate that our method achieves lower distortion, higher time efficiency, and better error-correcting performance.
Funding Information
  • National Natural Science Foundation of China (62371145)
  • National Natural Science Foundation of China (62441237)
  • National Natural Science Foundation of China (62261160653)
  • Natural Science Foundation of Fujian Province, China (2024J01116)