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Communication over the AWGN Channel

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Communication Principles for Data Science

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

In this section, we will cover two main topics. Firstly, we will discuss the logistics of the book, including its organization and structure. Secondly, we will provide a brief overview of the book, including the story of how communication theory was developed and what topics will be covered in the book.

Communication is the transfer of information from one end to another, and there exists a fundamental limit on the amount of information that can be transmitted reliably.

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Notes

  1. 1.

    Do not mistake the term “code” used in communication literature for computer programming languages like Python or C++. In this context, code refers to a transmission scheme.

  2. 2.

    The meaning of without loss of generality is that the general case can readily be boiled down to a simple case with some proper modification.

  3. 3.

    For simplicity of analysis, we assume that for the event \(y=0\), \(\hat{b}\) is decided to be 0 although we should flip a coin in the case as per the NN rule. Since the event has measure-zero (the probability of the event being occurred is 0), the error analysis remains the same.

  4. 4.

    It is the name of the technology for a digital broadcast system, standing for Digital Multimedia Broadcasting.

  5. 5.

    A rough definition of the law of large numbers is that the empirical mean of i.i.d. random variables approaches the true mean as the number of involved random variables increases. We will learn about the formal definition in Part III. If you want to know about it now, see Problems 8.1, 8.2 and 8.3.

  6. 6.

    The volume of an n-dimensional sphere of radius r is proportional to \(r^n\).

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Authors and Affiliations

  1. KAIST, Daejeon, Korea (Republic of)

    Changho Suh

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  1. Changho Suh
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Correspondence to Changho Suh .

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Suh, C. (2023). Communication over the AWGN Channel. In: Communication Principles for Data Science. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-19-8008-4_1

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  • DOI: https://doi.org/10.1007/978-981-19-8008-4_1

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-8007-7

  • Online ISBN: 978-981-19-8008-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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