Information theory is a mathematical framework for quantifying the transmission, processing, and storage of information.
Information theory has profound implications and applications across various domains, providing the theoretical foundation for understanding and optimizing how information is communicated and processed.
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Entropy: Often referred to as Shannon entropy, it measures the average amount of uncertainty or surprise associated with random variables. In essence, it quantifies the amount of information contained in a message or dataset.
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Information: In information theory, information is defined as the reduction in uncertainty. When you receive a message, the amount of information it provides is related to how much it reduces your uncertainty about the subject.
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Mutual Information: This measures the amount of information that two random variables share. It quantifies the reduction in uncertainty about one variable given knowledge of the other.
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Channel Capacity: This is the maximum rate at which information can be reliably transmitted over a communication channel. It is determined by the channel’s bandwidth and noise characteristics.
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Data Compression: Information theory provides the basis for data compression techniques, which aim to reduce the size of data without losing essential information. Lossless compression (e.g., ZIP) and lossy compression (e.g., JPEG) are two types of compression.
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Error Detection and Correction: Information theory also deals with methods for detecting and correcting errors in data transmission, ensuring that information can be accurately received even in the presence of noise.
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Rate-Distortion Theory: This aspect of information theory deals with the trade-offs between the fidelity of data representation and the amount of compression, which is crucial in applications like audio and video compression.