Generally speaking, a communication channel refers to a medium through which an information-bearing signal is corrupted by noise and distortion. A communication channel may result from data storage over time or data transmission through space. A primary task for communication engineers is to mathematically characterize the channel to facilitate the design of appropriate detection and coding systems. In this dissertation, two different channel modeling challenges for ultra-high density magnetic storage are investigated: two-dimensional magnetic recording (TDMR) and bit-patterned magnetic recording (BPMR). In the case of TDMR, we characterize the error mechanisms during the write/read process of data on a TDMR medium by a finite-state machine, and then design a state-based detector that provides soft decisions for use by an outer decoder. In the case of BPMR, we employ an insertion/deletion (I/D) model. We propose a LDPC-CRC product coding scheme that enables the error detection without the involvement of Marker codes specifically designed for an I/D channel. We also propose a generalized Gilbert-Elliott (GE) channel to approximate the I/D channel in the sense of an equivalent I/D event rate. A lower bound of the channel capacity for the BPMR channel is derived, which supports our claim that commonly used error-correction codes are effective on the I/D channel under the assumption that I/D events are limited to a finite length. Another channel model we investigated is perpendicular magnetic recording model. Advanced signal processing for the pattern-dependent-noise-predictive channel detectors is our focus. Specifically, we propose an adaptive scheme for a hardware design that reduces the complexity of the detector and the truncation/saturation error caused by a fix-point representation of values in the detector. Lastly, we designed a sequence detector for compressively sampled Bluetooth signals, thus allowing data recovery via sub-Nyquist sampling. This detector skips the conventional step of reconstructing the original signal from compressive samples prior to detection. We also propose an adaptive design of the sampling matrix, which almost achieves Nyquist sampling performance with a relatively high compression ratio. Additionally, this adaptive scheme can automatically choose an appropriate compression ratio as a function of.

This textbook covers the theoretical background of one- and multidimensional signal processing, statistical analysis and modelling, coding and information theory with regard to the principles and design of image, video and audio compression systems. The theoretical concepts are augmented by practical examples of algorithms for multimedia signal coding technology, and related transmission aspects. On this basis, principles behind multimedia coding standards, including most recent developments like High Efficiency Video Coding, can be well understood. Furthermore, potential advances in future development are pointed out. Numerous figures and examples help to illustrate the concepts covered. The book was developed on the basis of a graduate-level university course, and most chapters are supplemented by exercises. The book is also a self-contained introduction both for researchers and developers of multimedia compression systems in industry.

Constrained codes for digital storage systems are studied. A method for improving signal detection in digital magnetic recording systems is also investigated. The bit stuffing algorithm is a technique for coding constrained sequences by the insertion of bits into an arbitrary data sequence. This approach was previously introduced and applied to the family of $(d, k)$ constraints. Results show that the maximum average rate of the bit stuffing code achieves the Shannon capacity when $k=d+1$ or $k=\infty$, and fails to achieve capacity for all other $(d, k)$ pairs. A modification to the bit stuffing algorithm is proposed that is based on the addition of controlled bit flipping. It is shown that the modified scheme achieves improved average rates over bit stuffing for most $(d, k)$ constraints. All $(d, k)$ constraints for which this scheme produces codes with an average rate equal to the Shannon capacity are determined. A general framework for the construction of $(d, k)$-constrained codes from variable-length source codes is presented. Optimal variable-length codes under the general framework are investigated. The construction of constrained codes from variable-length source codes for encoding unconstrained sequences of independent but biased (as opposed to equiprobable) bits is also considered. It is shown that one can use the Tunstall source coding algorithm to generate optimal codes for a partial class of $(d, k)$ constraints. Bit-stuffing schemes which encode arbitrary inputs into two-dimensional (2-D) constrained arrays are presented. The class of 2-D $(d, \infty)$ constraints as well as the `no isolated bits' constraint are considered. The proposed schemes are based on interleaving biased bits with multiple biases into a 2-D array, while stuffing extra bits when necessary. The performance of the suggested schemes is studied through simulations. A method for joint detection and decoding of coded transmission over magnetic recording channels is considered. The standard framework of turbo equalization is modified to account for the colored noise present in high-density magnetic recording systems. The modified scheme incorporates a noise prediction algorithm, which iteratively and selectively whitens the noise, while utilizing the information produced by the turbo equalization scheme. Simulation results demonstrate the performance improvements obtained by the proposed scheme.

Expertly unraveling the mysteries and allure of signals, this book explores their profound impact on modern life. From classical techniques to cutting-edge advancements, this comprehensive exploration delves into fundamental concepts such as amplitude, frequency, and phase. With meticulous research and insightful analysis, the author guides readers through topics like Fourier analysis, sampling, quantization, and signal filtering. The book highlights the dynamic relationship between time and frequency domains, statistical signal processing techniques, and the fascinating realm of non-classical signal processing, including wavelet transforms and compressed sensing, and explores diverse applications in audio, speech, image and video processing, biomedical analysis, communications, and sensor fusion. Highlighting emerging trends and future directions, the book illuminates the challenges, opportunities, and potential breakthroughs in signal processing research.

This comprehensive text is a revised and greatly expanded second edition of a book first published in 1987, and provides a thorough introduction to the complex fields of signal coding and signal processing. Among the key topics covered are: the fundamentals of pulse code modulation; modern data compression techniques; block and convolutional error control codes; transmission coding techniques; digital filters; infinite and finite impulse response filters; adaptive filters; and fast Fourier transform theory, implementation and applications. Complete with problems and solutions, and containing over 230 diagrams, this textbook will be invaluable to third and fourth year undergraduates in electronic, electrical or communication engineering. It will also act as a useful reference for anyone working in this technologically important field.

The field of digital signal processing (DSP) has spurred developments from basic theory of discrete-time signals and processing tools to diverse applications in telecommunications, speech and acoustics, radar, and video. This volume provides an accessible reference, offering theoretical and practical information to the audience of DSP users. This immense compilation outlines both introductory and specialized aspects of information-bearing signals in digital form, creating a resource relevant to the expanding needs of the engineering community. It also explores the use of computers and special-purpose digital hardware in extracting information or transforming signals in advantageous ways. Impacted areas presented include: Telecommunications Computer engineering Acoustics Seismic data analysis DSP software and hardware Image and video processing Remote sensing Multimedia applications Medical technology Radar and sonar applications This authoritative collaboration, written by the foremost researchers and practitioners in their fields, comprehensively presents the range of DSP: from theory to application, from algorithms to hardware.

Digital Signal Processing: Applications to Communications and Algebraic Coding Theories discusses the design of computationally efficient digital signal processing algorithms over finite fields and the relation of these algorithms to algebraic error-correcting codes. The book provides chapters that cover such topics as signal processing techniques employed for modeling, synthesis, and analysis; systems of bilinear forms; efficient finite field algorithms; the design and study of long length cyclic convolutions and some preliminary results on their relation to linear codes; the study of the algebraic structure of the class of linear codes obtained from bilinear cyclic and aperiodic convolution algorithms over the finite field of interest; and the concept of a generalized hybrid Automatic- Repeat-Request (ARQ) scheme for adaptive error control in digital communication systems. Engineers, mathematicians, and computer scientists will find the text invaluable.