Constant-weight code: Difference between revisions

Revision as of 13:08, 4 December 2014

Revision as of 13:58, 4 December 2014

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| authors=W.J.Bainbridge, A.Bardsley, R.W.McGuffin

}}</ref> used in delay insensitive circuits. For these codes, <math>n=N,~ d=2,~ w=1</math> and <math>A(n, d, w) = n</math>.

Some of the more notable uses of one-hot codes include

[[biphase mark code]] uses a 1 of 2 code;

[[pulse-position modulation]] uses a 1 of n code;

[[address decoder]],

etc.

== Balanced code ==

In [[coding theory]], a '''balanced code''' is a [[binary numeral system|binary]] [[forward error correction]] code for which each codeword contains an equal number of zero and one bits. Balanced codes have been introduced by [[Donald Knuth]];<ref name="knuth">{{cite journal|author=D.E. Knuth|title=Efficient balanced codes|journal=IEEE Transactions on Information Theory|volume=32|issue=1|pages=51–53|date=January 1986|doi=10.1109/TIT.1986.1057136|url=http://www.costasarrays.org/costasrefs/knuth86efficient.pdf}}</ref> they are a subset of so-called unordered codes, which are codes having the property that the positions of ones in a codeword are never a subset of the positions of the ones in another codeword. Like all unordered codes, balanced codes are suitable for the detection of all [[unidirectional error]]s in an encoded message. Balanced codes allow for particularly efficient decoding, which can be carried out in parallel.<ref name="knuth"/><ref name="optimal">{{cite journal|author1=Sulaiman Al-Bassam|author2=Bella Bose|title=On Balanced Codes|journal=IEEE Transactions on Information Theory|volume=36|issue=2|pages=406–408|date=March 1990|doi=10.1109/18.52490}}</ref>

Some of the more notable uses of balanced-weight codes include

[[6b/8bbiphase encodingmark code]] uses a 41 of 82 code;

[[6b/8b encoding]] uses a 4 of 8 code;

the [[Hadamard code]] is a <math>2^k/2</math> of <math>2^k</math> code (except for the zero codeword),

etc.

== m of n codes==

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Some of the more notable uses of constant-weight codes, other than the one-hot and balanced-weight codes already mentioned above, include

[[biphase mark code]] uses a 1 of 2 code;

[[pulse-position modulation]] uses a 1 of n code;

[[Code 39]] uses a 3 of 9 code;

[[6b/8b encoding]] uses a 4 of 8 code;

[[bi-quinary coded decimal]] code uses a 2 of 7 code,

the [[HadamardTwo-out-of-five code|2 of 5 code]],

etc.