Advanced Coding for Multidimensional Channels

University Of California-San Diego, La Jolla CA

Investigators

Abstract

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.