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Coding Theory Basics

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Binary Code

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A coding system using the binary digits 0 and 1 to represent a letter, digit, or other character in a computer or other electronic device.

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Hamming Distance

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

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Block Code

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A coding scheme in which a fixed-length block of bits is encoded into a fixed-length block of n bits, where n is greater than the original block length.

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Information Rate

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The rate at which information can be transmitted over a communication channel, measured in bits per unit time.

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Error Detection

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The process of identifying and correcting errors in data transmission or storage.

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Parity Bit

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A bit that is added to a group of bits to ensure that the number of bits with the value one is even or odd.

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Cyclic Redundancy Check (CRC)

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An error-detecting code commonly used in digital networks and storage devices to detect accidental changes to raw data.

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Hamming Code

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A set of error-correction code that can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors.

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Channel Capacity

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The tightest upper bound on the amount of information that can be reliably transmitted over a communications channel.

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Shannon's Theorem

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A theorem in information theory which states that for any given degree of noise contamination of a communication channel, it is possible to transmit information nearly error-free up to a computable maximum rate through the channel.

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Coding Gain

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The measure of the improvement in signal-to-noise ratio of a communication system from the use of coding.

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Maximum Likelihood Decoding

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A method of decoding a block of encoded data to choose the most likely original data.

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