Chapter 1: Introduction
* Discusses the importance of communication and the need for a mathematical theory to understand it.
* Introduces key concepts such as information, source, and destination.
Example: A message (e.g., "Hello, how are you?") is sent from a speaker (source) to a listener (destination) through a communication channel (e.g., air).
Chapter 2: The Discrete Case
* Presents the foundational concepts of discrete communication, where information is represented by a finite set of symbols.
* Introduces entropy as a measure of information content.
Example: A binary communication system (e.g., a fax machine) using 0 and 1 as symbols. The entropy of this system is 1 bit per symbol.
Chapter 3: The Continuous Case
* Extends the concepts of Chapter 2 to continuous information, such as the waveforms in an analog signal.
* Introduces the Gaussian distribution as a fundamental statistical model for continuous information.
Example: A radio broadcasting an audio signal. The entropy of the Gaussian distribution used to model the signal determines the maximum amount of information that can be transmitted.
Chapter 4: The Channel
* Examines the characteristics of communication channels and their impact on information transmission.
* Introduces concepts such as bandwidth, noise, and channel capacity.
Example: A telephone line with a limited bandwidth and background noise. The channel capacity limits the rate at which information can be transmitted without distortion.
Chapter 5: Coding
* Discusses methods for encoding and decoding information to improve its transmission efficiency.
* Presents techniques such as source coding (compression) and channel coding (error correction).
Example: A compression algorithm used to reduce the size of a JPEG image before sending it over a network.
Chapter 6: Reliability
* Explores the concept of reliability in communication and the techniques used to achieve it.
* Introduces concepts such as error detection and correction codes.
Example: A fire alarm system using a redundant communication channel to ensure that an alarm is received in the event of a channel failure.
Chapter 7: Application to General Systems
* Extends the theory of communication to general systems, including non-electrical systems and biological systems.
* Explores the implications of the theory for understanding and designing complex systems.
Example: The use of information theory to analyze the efficiency of communication between neurons in the human brain.
