Embedding with syndrome coding based on BCH codes

Abstract

With Matrix Embedding based on Hamming Codes, coding theory has entered the field of steganography. Even though this class of structured codes had been used successfully in practical systems to minimize the number of embedding changes, thus maximizing embedding efficiency, further developments, such as Wet Paper Codes, were based on random codes instead.This paper redraws attention to structured codes, which are built according to deterministic rules. In particular, we study BCH Codes for embedding with syndrome coding, using either a structured matrix Hk x n as in Matrix Embedding, or a generator polynomial g(χ). We propose different approaches for embedding without locked elements, which differ in the tradeoff reached between embedding complexity and efficiency.As some practical systems allow more secure steganography if embedding constraints -- in terms of locked elements -- are respected, we demonstrate how BCH Codes can be employed in a Wet Paper Codes scenario as well. Based on a deduced analogy between code rate and the maximum number of lockable elements, we can find appropriate code parameters for a given fraction of locked elements in the cover, complexity constraints, and desired probability of successful embedding.