We are undergoing a revolution in data. The ever-growing amount of information in our world has created an unprecedented demand for ultra-reliable, affordable, and resource-efficient data storage systems. Error-correcting codes, as a critical component of any memory device, will play a crucial role in the future of data storage. One particular class of error-correcting codes, known as graph-based codes, has drawn significant attention in both academia and in industry. Graph-based codes offer superior performance compared to traditional algebraic codes. Recently, it has been shown that non-binary graph-based codes, which operate over finite fields rather than binary alphabets, outperform their binary counterparts and exhibit outstanding overall performance. For this reason, these codes are particularly suitable for emerging data storage systems. In this dissertation, we present a comprehensive combinatorial analysis of non-binary graph-based codes. We perform both finite-length and asymptotic analyses for these codes, providing a systematic framework to evaluate and optimize various families of non-binary graph-based codes. In the finite-length case, we provide a mathematical characterization of the error floor problem, including a general definition of absorbing sets over non-binary alphabets. We consider several structured low-density parity-check (LDPC) codes, including quasi-cyclic and spatially-coupled codes, as well as unstructured LDPC codes. We offer design guidelines for non-binary LDPC codes with outstanding performance in extremely low error-rate regimes; making them excellent candidates for data storage applications. In the asymptotic case, we provide a novel toolbox for the evaluation of families of non-binary graph-based codes. By utilizing insights from graph theory and combinatorics, we establish enumerators for a general family of graph-based codes which are constructed based on protographs. We provide asymptotic distributions of codewords and trapping sets for the family of protograph-based codes. Furthermore, we present an asymptotic enumeration of binary and non-binary elementary absorbing sets for regular code ensembles. The contributions of this dissertation can potentially impact a broad range of data storage and communication technologies that require excellent performance in high-reliability regimes.

Using easy-to-follow mathematics, this textbook provides comprehensive coverage of block codes and techniques for reliable communications and data storage. It covers major code designs and constructions from geometric, algebraic, and graph-theoretic points of view, decoding algorithms, error control additive white Gaussian noise (AWGN) and erasure, and dataless recovery. It simplifies a highly mathematical subject to a level that can be understood and applied with a minimum background in mathematics, provides step-by-step explanation of all covered topics, both fundamental and advanced, and includes plenty of practical illustrative examples to assist understanding. Numerous homework problems are included to strengthen student comprehension of new and abstract concepts, and a solutions manual is available online for instructors. Modern developments, including polar codes, are also covered. An essential textbook for senior undergraduates and graduates taking introductory coding courses, students taking advanced full-year graduate coding courses, and professionals working on coding for communications and data storage.

Ultra-Reliable and Low-Latency Communications (URLLC) Theory and Practice Comprehensive resource presenting important recent advances in wireless communications for URLLC services, including device-to-device communication, multi-connectivity, and more Ultra-Reliable and Low-Latency Communications (URLLC) Theory and Practice discusses the typical scenarios, possible solutions, and state-of-the-art techniques that enable URLLC in different perspectives from the physical layer to higher-level approaches, aiming to tackle URLLC’s challenges with both theoretical and practical approaches, which bridges the lacuna between theory and practice. With long-term contributions to the development of future wireless networks, the text systematically presents a thorough study of the novel and innovative paradigm of URLLC; basic requirements are covered, along with essential definitions, state-of-the-art technologies, and promising research directions of URLLC. To aid in reader comprehension, tables, figures, design schematics, and examples are provided to illustrate abstract engineering concepts and make the text more accessible to a broader readership, and corresponding case studies are included in the last part of the book. Fundamental problems in URLLC, including designing building blocks for URLLC, radio resource management in URLLC, resource optimization, network availability guarantee, and coexisting with other future mobile networks, are also discussed. In Ultra-Reliable and Low-Latency Communications (URLLC) Theory and Practice, readers can expect to find detailed information on: BCH and analog codes, stable matching, OFDM demodulation and turbo coding, and semi-blind receivers for URLLC MIMO-NOMA with URLLC, PHY and MAC layer technologies for URLLC, and Network slicing or SDN for URLLC and eMBB Integrating theoretical knowledge into deep learning for URLLC, Energy-Latency tradeoff in URLLC, and Downlink transmission for URLLC under physical layer aspects Resource allocation for multi-user downlink URLLC, HARQ optimization for 5G URLLC, and Multi-Access edge computing with URLLC A unique resource with comprehensive yet accessible coverage of a complicated subject, Ultra-Reliable and Low-Latency Communications (URLLC) Theory and Practice is an ideal resource for a large and diverse population of researchers and practitioners in engineering, computer scientists, and senior undergraduate and graduate students in related programs of study.

This book constitutes the refereed proceedings of the 40th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2014, held in Nový Smokovec, Slovakia, in January 2014. The 40 revised full papers presented in this volume were carefully reviewed and selected from 104 submissions. The book also contains 6 invited talks. The contributions covers topics as: Foundations of Computer Science, Software and Web Engineering, as well as Data, Information and Knowledge Engineering and Cryptography, Security and Verification.

This new edition has been extensively revised to reflect the progress in error control coding over the past few years. Over 60% of the material has been completely reworked, and 30% of the material is original. Convolutional, turbo, and low density parity-check (LDPC) coding and polar codes in a unified framework Advanced research-related developments such as spatial coupling A focus on algorithmic and implementation aspects of error control coding

By using computer simulations in research and development, computational science and engineering (CSE) allows empirical inquiry where traditional experimentation and methods of inquiry are difficult, inefficient, or prohibitively expensive. The Handbook of Research on Computational Science and Engineering: Theory and Practice is a reference for interested researchers and decision-makers who want a timely introduction to the possibilities in CSE to advance their ongoing research and applications or to discover new resources and cutting edge developments. Rather than reporting results obtained using CSE models, this comprehensive survey captures the architecture of the cross-disciplinary field, explores the long term implications of technology choices, alerts readers to the hurdles facing CSE, and identifies trends in future development.

This book constitutes the refereed proceedings of the 5th International Conference, ICMT 2012, held in Prague, Czech Republic, in May 2012, co-located with TOOLS 2012 Federated Conferences. The 18 full papers presented together with one invited paper were carefully revised and selected from numerous submissions. Topics addressed are such as testing, typing and verification; bidirectionality; applications and visualization; transformation languages, virtual machines; pattern matching; and transformations in modelling, reutilization.