This paper explores the data hiding schemes which are based on the principle of matrix embedding. Under the same embedding rate, the efficiency of each data hiding scheme is evaluated by the metric of average embedding efficiency. In the literature, both the row-column embedding and the weight approximation embedding algorithms are sub-optimal solutions for the product code-based data hiding problem. For the former, it is still based on the concept of one-dimensional (1-D) toggle syndrome, and the concept of two-dimensional (2-D) toggle syndrome is directly adopted for the latter one. Data hiding with multiple embedding channels is the practice of hiding messages into hidden media many times. Here, two multi-channel embedding-based data hiding techniques—one is the 1-D toggle syndrome-based embedding scheme (1DTS-1), and the other is the improved weight approximation-based embedding scheme (2DTS-1), are presented. In the former, the proposed one-off decision technique is used to determine the locations of the required modification bits, and the amount of modification will be reduced through utilizing the characteristics of the linear code. With the technique of the former, in the latter, the amount of modification bits can be further reduced because that a toggle array with better structure is generated, which is more suitable for being assigned as the initial toggle array while applying the weight approximation approach. The experimental results show our proposed hybrid 1-D/2-D toggle syndrome-based embedding scheme (2DTS-1) has increased the embedding efficiency by 0.1149 when compared to the weight approximation embedding algorithm. Further, the embedding efficiency of the latter one can be further and significantly enhanced through the Hamming+1 technique.
On a Decomposition Method in the Problem of Operation Speed for a Linear Discrete System with Bounded Control
