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A measure of the unpredictability or randomness of a system, typically denoted as $H(X)$ for a discrete random variable X.

The maximum rate at which information can be reliably transmitted over a communication channel, represented as $C$ and given by the Shannon-Hartley theorem.

A fundamental theorem stating that there exists a coding technique that allows the transmission of data over a noisy channel at rates up to the channel capacity with an arbitrarily small error probability.

The amount of information that one random variable contains about another random variable, often denoted as $I(X;Y)$.

The portion of information that is not necessary to understand the content, often a result of repeating patterns or predictability.

The unwanted alterations in the signal during transmission, which may lead to errors in the received data.

The process of encoding information from a source in a way that removes redundancy, making it more compact without losing essential information.

A measure used to compare the level of a desired signal to the level of background noise, often expressed in decibels (dB).

The number of positions at which the corresponding symbols are different in two strings of equal length.

The minimum sampling rate, twice the highest frequency present in the signal, required to reconstruct a continuous signal from its samples without loss of information, given by $2B$ where $B$ is the highest frequency.

The continuous counterpart of entropy for continuous random variables, measuring the randomness or unpredictability.

A data compression method that uses inexact approximations for representing the content that may not allow for a perfect reconstruction but results in smaller file sizes.

Techniques in digital communications to detect and correct errors in data transmission and storage.

The process of encoding information using fewer bits, which may involve lossless or lossy methods.

A formula to calculate the maximum rate of information ($C$) that can be transmitted over a communications channel of a specified bandwidth in the presence of noise, given as

The improvement in signal-to-noise ratio due to the implementation of an error-correcting code, contributing to more reliable transmission.

A framework in information theory that deals with the trade-off between the data rate of a source and the distortion (or accuracy) of the reconstructed data.

A protocol for error control in data transmission, where the receiver detects errors and requests retransmission of corrupted data.

The theorem states that a source can be compressed to its entropy $H(X)$ (in bits) without loss of information, defining the fundamental limit of lossless data compression.

A data compression algorithm that allows the original data to be perfectly reconstructed from the compressed data.

The speed at which information is transmitted over a channel, typically measured in bits per second (bps).

A method of encoding data in fixed-size blocks to enable error detection and correction for reliable transmission.

An error-correcting code where the encoded output is a function of the current and previous input bits, leading to overlapping code words that are processed sequentially.

A system of error control for data transmission that uses error-correcting codes to detect and correct errors at the receiver without the need for retransmission.