Approaching maximum embedding efficiency on small covers using Staircase-Generator codes

We introduce a new family of binary linear codes suitable for steganographic matrix embedding. The main characteristic of the codes is the staircase random block structure of the generator matrix. We propose an efficient list decoding algorithm for the codes that finds a close codeword to a given random word. We provide both theoretical analysis of the performance and stability of the decoding algorithm, as well as practical results. Used for matrix embedding, these codes achieve almost the upper theoretical bound of the embedding efficiency for covers in the range of 1000 - 1500 bits, which is at least an order of magnitude smaller than the values reported in related works.