Source and Channel Coding for Multidimensional Channels

University Of California-San Diego, La Jolla CA

Investigators

Abstract

This project studies the theory of multidimensional channels and investigates effective coding techniques for such channels. The coding techniques 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 storage. These are the storage devices of the future. An important application of this research within the next few years is the storage of massive amounts of still imagery and video on two-dimensional media. This will likely extend to three-dimensional and four-dimensional (the fourth dimension is wavelength) devices over the next 5 to 10 years. Such multidimensional devices will require a shift in paradigm, 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. There is much to be gained by coding for multidimensional channels, but the problems associated with such channels are considerably more challenging than their one-dimensional counterparts. Interesting technical problems arise due to the spatially dependent nature of errors in multidimensional storage media. New error-correcting codes and interleaving techniques are needed to effectively protect data stored on such media. The physical properties of optical and holographic recording channels call for a new theory of constrained coding in multiple dimensions. New joint source-channel coding techniques and theory are needed to maximize the recovered source fidelity for images and video stored on multidimensional devices while keeping the storage density as high as possible. Inparticular, the storage capacity of multidimensional devices can be greatly increased at the expense of a less reliable recovery of the stored imagery/video than is current practice for the storage of data. This project studies the tradeoff between increased storage capacity and quantitative loss in fidelity of the reproduced source signal. The main topics being investigated for multidimensional channels are: (1) Error-correcting codes, (2) Interleaving techniques, (3) Soft-decision decoding, (4) Capacity computation for constrained channels, (5)~Encoders and decoders for specific constraints, (6) Joint source-channel coder design.