View source for Code rate

{{Short description|Non-redundant proportion of an error correction code data stream}}
{{one source |date=April 2024}}
[[File:Coderateblock.png|400px|thumb|right|Different code rates ([[Hamming code]]).]]
In [[telecommunication]] and [[information theory]], the '''code rate''' (or '''information rate'''<ref>Huffman, W. Cary, and Pless, Vera, ''Fundamentals of Error-Correcting Codes'', Cambridge, 2003.</ref>) of a [[forward error correction]] code is the proportion of the data-stream that is useful (non-[[Redundancy (information theory)|redundant]]). That is, if the code rate is <math>k/n</math> for every {{mvar|k}} bits of useful information, the coder generates a total of {{mvar|n}} bits of data, of which <math>n-k</math> are redundant. 

If {{mvar|R}} is the [[gross bit rate]] or [[data signalling rate]] (inclusive of redundant error coding), the [[net bit rate]] (the useful bit rate exclusive of [[error correction code]]s) is <math>\leq R \cdot k/n</math>. 

For example: The code rate of a [[convolutional code]] will typically be {{1/2}}, {{2/3}}, {{3/4}}, {{frac|5|6}}, {{frac|7|8}}, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the [[octet (computing)|octet]] oriented [[Reed Solomon]] [[block code]] denoted RS(204,188) is 188/204, meaning that {{math|1=204 &minus; 188 = 16}} redundant octets (or bytes) are added to each block of 188 octets of useful information. 

A few error correction codes do not have a fixed code rate—[[rateless erasure code]]s.

Note that [[bit/s]] is a more widespread [[unit of measurement]] for the [[information rate]], implying that it is synonymous with ''net bit rate'' or ''useful bit rate'' exclusive of error-correction codes.

==See also==
* [[Entropy rate]]
* [[Information rate]]
* [[Punctured code]]

==References==
{{reflist}}

[[Category:Information theory]]
[[Category:Rates]]


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