StegoCoder: Learning Channel for Steganographic Coding

Image steganography hides a message in a cover image with minimal perceptible distortion, producing a stego image from which an authorized receiver can recover the message. Robust steganography additionally requires recovery after the stego image is perturbed. Classical steganographic codes operate close to the rate-distortion bound, but on a fixed binary projection of the cover, typically its least-significant bit planes, in which the payload is destroyed by even mild perturbations. Neural steganography can be trained end-to-end to survive specific perturbations, but lacks the explicit rate-distortion control that coding theory provides. StegoCoder combines the two. A steganographic code first embeds the message into a fixed binary sequence and produces a binary stego sequence. A neural renderer then synthesizes the stego image from the cover image and the resulting binary stego. At the receiver, a learned bit predictor outputs soft estimates of the binary stego from the perturbed image, and the code decodes the message. The networks thus learn a reliable binary channel over which a classical steganographic code operates, splitting the problem into learning the channel and embedding the message efficiently over a binary cover. With a nested polar code, the same code acts as a lossy source code at the sender and as a channel code at the receiver, giving explicit control over the trade-off between embedding distortion and robustness. On CelebA-HQ, StegoCoder recovers most of the $500$ test images without a single bit error under additive Gaussian noise of standard deviation $10^{-2}$ at $1$ and $2$ bits per pixel (bpp) and $5\cdot 10^{-3}$ at $3$ and $4$ bpp, where least-significant-bit embedding, per-image optimization and end-to-end neural approaches recover none and quantization index modulation substantially fewer. A per-image refinement of the stego image further extends robustness across different payloads and co-training the scheme with the neural polar decoder decreases the distortion.