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Coding Theory Basics
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Binary Code
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.
Hamming Distance
The number of positions at which the corresponding symbols are different in two strings of equal length.
Error Detection
The process of identifying and correcting errors in data transmission or storage.
Parity Bit
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.
Cyclic Redundancy Check (CRC)
An error-detecting code commonly used in digital networks and storage devices to detect accidental changes to raw data.
Hamming Code
A set of error-correction code that can detect up to two-bit errors or correct one-bit errors without detection of uncorrected errors.
Channel Capacity
The tightest upper bound on the amount of information that can be reliably transmitted over a communications channel.
Shannon's Theorem
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.
Coding Gain
The measure of the improvement in signal-to-noise ratio of a communication system from the use of coding.
Maximum Likelihood Decoding
A method of decoding a block of encoded data to choose the most likely original data.
Block Code
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.
Information Rate
The rate at which information can be transmitted over a communication channel, measured in bits per unit time.
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