Coding, Detection, and Inference in Multiple Dimensions
Creators: name: University Of California Office Of The President
Publisher: name: University of California Office of the President
publisherIdentifier: https://ror.org/00dmfq477
publisherIdentifierScheme: ROR
Year: 2024

description: The ability to reliably store, retrieve, process, and visualize massive amounts of information is of paramount importance to national security and the continued growth of the U.S. economy. Advanced data storage and transmission techniques represent key enabling technologies for the required computing and communication infrastructure. Currently, the majority of storage devices and transmission links utilize coding, modulation, and signal processing schemes that operate on one-dimensional data sequences. However, the explosive demand for high-speed transfer of large amounts of structured information to and from both local and network-attached storage devices is driving technology in the direction of a multidimensional perspective. An example of this is two-dimensional “page-oriented” holographic recording technology, which is likely to evolve into three-dimensional (volumetric) recording and conceivably to four-dimensional designs, the fourth dimension being the wavelength of the optical beam. Such technology trends demand the investigation of coding and detection methods in multiple dimensions. Probabilistic coding and detection techniques, along with algebraic error-correcting coding, have essentially solved the problem of reliable recording and communication over certain classes of one-dimensional channels. The research challenges addressed by this project stem from the fact that the analytical methods and algorithmic techniques that have been so successful in the one-dimensional scenario are not obviously extendible to higher dimensions. One objective of this project is to explore the application of iterative probabilistic inference algorithms on higher-dimensional graphical models to the problem of decoding and detection of multidimensional codes and channels. As part of this, the relationship of linear programming algorithms to iterative graph-based algorithms, as well as their potential for practical implementation, will be investigated. Another objective is to develop multidimensional interleaving and algebraic coding methodologies that improve resilience to spatially correlated errors with various connectivity structures, and to determine whether the structure of the graphical models of these codes can be exploited in their decoding. To achieve these aims, the investigators will use methods and approaches suggested by their recent work. Specifically, they will further explore techniques for identifying two-dimensional graphical models that support efficient and exact algorithms for probabilistic inference. They will also evaluate the performance of detection algorithms based upon generalized belief propagation on graphical models representing multidimensional coded, finite-memory channels. Advances in the analysis and implementation of linear programming decoders will provide tools for elucidating their error-rate performance and their relationship to message-passing decoders, while suggesting the possible applicability of these algorithms in practical systems. Interleaving techniques and error-correcting codes developed to combat certain types of cluster errors in two dimensions will be improved and generalized to higher dimensions. In particular, decoding algorithms that more effectively exploit the underlying graphical structure of multidimensional product codes will be investigated. The results of this project will influence the development of coding and detection methods for future information storage and transmission systems in which the data and channels are naturally represented by multidimensional graphical models. They will also advance fundamental understanding in several areas including information theory, probabilistic inference on graphs, and optimization theory. More broadly, this collaborative effort will create closer ties between LANL and UCSD in an emerging interdisciplinary field in which the two institutions have complementary expertise. It will raise the level of awareness at UCSD of DOE-relevant problems in information sciences and technology and it will help to provide unique training for graduate students in disciplines related to industrial and national security applications. The project should also set the stage for future research efforts at the Theory, Simulation and Computation (TSC) and Threat Reduction (TR) directorates at LANL in the areas of Information Processing, Multi-agent Simulation and Social Modeling.