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Processing, storing, and communicating information that originates as an analog phenomenon involve conversion of the information to bits. This conversion can be described by the combined effect of sampling and quantization. The digital representation in this procedure is achieved by first sampling the analog signal so as to represent it by a set of discrete-time samples and then quantizing these samples to a finite number of bits. Traditionally, these two operations are considered separately. The sampler is designed to minimize information loss due to sampling based on prior assumptions about the continuous-time input. The quantizer is designed to represent the samples as accurately as possible, subject to the constraint on the number of bits that can be used in the representation. The goal of this chapter is to revisit this paradigm by considering the joint effect of these two operations and to illuminate the dependence between them.
The purpose of this chapter is to set the stage for the book and for the upcoming chapters. We first overview classical information-theoretic problems and solutions. We then discuss emerging applications of information-theoretic methods in various data-science problems and, where applicable, refer the reader to related chapters in the book. Throughout this chapter, we highlight the perspectives, tools, and methods that play important roles in classic information-theoretic paradigms and in emerging areas of data science. Table 1.1 provides a summary of the different topics covered in this chapter and highlights the different chapters that can be read as a follow-up to these topics.
Learn about the state-of-the-art at the interface between information theory and data science with this first unified treatment of the subject. Written by leading experts in a clear, tutorial style, and using consistent notation and definitions throughout, it shows how information-theoretic methods are being used in data acquisition, data representation, data analysis, and statistics and machine learning. Coverage is broad, with chapters on signal acquisition, data compression, compressive sensing, data communication, representation learning, emerging topics in statistics, and much more. Each chapter includes a topic overview, definition of the key problems, emerging and open problems, and an extensive reference list, allowing readers to develop in-depth knowledge and understanding. Providing a thorough survey of the current research area and cutting-edge trends, this is essential reading for graduate students and researchers working in information theory, signal processing, machine learning, and statistics.