This project studies the theory of multidimensional channels and develop effective coding techniques for such channels. The coding techniques investigated are of three types: error-correction channel coding, constrained coding, and joint source-channel coding. Emphasis is placed on applications to two-dimensional magnetic and optical recording as well as three-dimensional holographic recording. These are the storage devices of the future.
The investigation involves code design, theoretical analysis, and computer simulation.
The main topic areas investigated for multidimensional channels are:
Interleaving techniques in two and three dimensions Multidimensional codes correcting cluster errors Constrained coding and defect avoidance for multidimensional media - Progressive source coding for multidimensional channels - Index assignment for multidimensional channels
Multidimensional storage devices require a completely new theory and new technical breakthroughs, since most of the existing theory for error-correcting codes, constrained codes, and source-channel codes was developed in the context of one-dimensional applications. The problems associated with multidimensional channels are usually much more challenging than their one-dimensional counterparts.
In particular, interesting technical problems arise due to the spatially dependent nature of errors and constraints in multidimensional recording media. New error-correcting codes and interleaving techniques are needed to effectively protect data stored on such media. The study of constrained coding for multidimensional channels is still in its infancy , and needs substantial further research to blossom into a theory. Joint source-channel coding techniques are needed to maximize the recovered source fidelity for images and video stored on multidimensional devices.
