Coding theory: Difference between revisions

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==History of coding theory==

{{see alsoexcerpt|History of information theory}}

InShannon’s 1948, [[Claude Shannon]] published "[[A Mathematical Theory of Communication]]", an article in two parts in the July and October issues of the ''Bell System Technical Journal''. This workpaper focuses on the problem of how to best to encode the [[information]] a sender wants to transmit. In this fundamental work he used tools in probability theory, developed by [[Norbert Wiener]], which were in their nascent stages of being applied to communication theory at that time. Shannon developed [[information entropy]] as a measure for the uncertainty in a message while essentially inventing the field of [[information theory]].

The [[binary Golay code]] was developed in 1949. It is an error-correcting code capable of correcting up to three errors in each 24-bit word, and detecting a fourth.

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# [[Reed–Muller code]]s

# [[Hamming bound|Perfect codes]]

# [[Locally Recoverablerecoverable Codescode]]

Block codes are tied to the [[sphere packing]] problem, which has received some attention over the years. In two dimensions, it is easy to visualize. Take a bunch of pennies flat on the table and push them together. The result is a hexagon pattern like a bee's nest. But block codes rely on more dimensions which cannot easily be visualized. The powerful (24,12) [[Binary Golay code|Golay code]] used in deep space communications uses 24 dimensions. If used as a binary code (which it usually is) the dimensions refer to the length of the codeword as defined above.

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{{main|Line code}}

A [[line code]] (also called digital baseband modulation or digital [[baseband]] transmission method) is a [[code]] chosen for use within a [[communications system]] for baseband [[transmission (telecommunications)|transmission]] purposes. Line coding is often used for digital data transport.

Line coding is often used for digital data transport. It consists of representing the [[Digital signal (electronics)|digital signal]] to be transported by an amplitude- and time-discrete signal that is optimally tuned for the specific properties of the physical channel (and of the receiving equipment). The [[waveform]] pattern of voltage or current used to represent the 1s and 0s of a digital data on a transmission link is called ''line encoding''. The common types of line encoding are [[Unipolar encoding|unipolar]], [[Polar encoding|polar]], [[Bipolar encoding|bipolar]], and [[Manchester encoding]].

==Other applications of coding theory==