Constrained coding and signal processing for holography

The increasing demand for high density storage devices has led to innovative data recording paradigms like optical holographic memories and patterned media. In holographic memories, data is stored in the form of two-dimensional pages within the volume of a recording material. These memories promise ultra-high volumetric densities (1Tb/cm3) and ultra-fast readout speeds (1Gb/s) and could be the future hard drives based on nanoscale technology. To realize the potential of these devices, significant research needs to be done in many multi-disciplinary areas, such as material science, optics, information theory, and signal processing. Consequently, coding theorists and signal processing practitioners are interested in developing efficient two-dimensional constrained codes, error correcting codes, and signal processing algorithms for holographic systems.; Holographic data storage is just one application where two-dimensional coding theory can be put into practice. From a theoretical perspective, the study of two- and higher-dimensional constrained systems is an active area of research in symbolic dynamics, a branch of mathematics dealing with discrete dynamical systems. The applications of this theory have deep consequences in other areas, such as mathematical physics, finite automata theory, and languages in computer science. Thus, it is important to understand the fundamental limits of two-dimensional constrained systems.; The theory behind one-dimensional constrained channels is well known. There are a number of algorithms for constructing codes with rates as close to capacity as desired. However, computing the capacity and constructing codes for higher-dimensional constrained systems is an open problem. There are a few cases where tight bounds for two-dimensional capacity are known. Also, there are hardly any efficient algorithms for constructing two-dimensional codes.; In this thesis, we propose tiling algorithms for constructing a few classes of two-dimensional runlength-limited codes on a rectangular lattice and derive bounds for the channel capacity. We present sequential nested-block coding algorithms with rates close to the derived capacity lower bounds. The proposed tiling algorithms are constructive and have low encoding complexities. Motivated by recent advances in localized holography, we generalize our bounds and coding algorithms for two-dimensional M-ary runlength-limited channels.; The storage and retrieval of information from a holographic drive can be modeled as data transmission over a noisy communications channel. We derive a lower bound for the capacity of holographic channels and analyze the density versus multiplexing trade-off. This result is useful for deciding the number of recorded pages and for choosing the right code for maximizing the volumetric storage density.; The pixel misregistration problem is an important topic in signal reconstruction theory. In a holographic system, the spatial light modulator (SLM) and the detector arrays are not perfectly aligned. This leads to interpixel crosstalk. We develop a channel model and propose an algorithm for recovering data bits in the presence of pixel misregistration and noise.