Multimedia data hiding or steganography is a means of communication using subliminal channels. The resource for the subliminal communication scheme is the distortion of the original content that can be tolerated. This thesis addresses two main issues of steganographic communication schemes:

1. How does one maximize the distortion introduced without affecting fidelity of the content?

2. How does one efficiently utilize the resource (the distortion introduced) for communicating as many bits of information as possible? In other words, what is a good signaling strategy for the subliminal communication scheme?

Close to optimal solutions for both issues are analyzed. Many techniques for the issue for maximizing the resource, viz, the distortion introduced imperceptibly in images and video frames, are proposed. Different signaling strategies for steganographic communication are explored, and a novel signaling technique employing a floating signal constellation is proposed. Algorithms for optimal choices of the parameters of the signaling technique are presented.

Other application specific issues like the type of robustness needed are taken into consideration along with the established theoretical background to design optimal data hiding schemes. In particular, two very important applications of data hiding are addressed - data hiding for multimedia content delivery, and data hiding for watermarking (for proving ownership). A robust watermarking protocol for unambiguous resolution of ownership is proposed.