Code rate

In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is k / n {\displaystyle k/n} , for every k bits of useful information, the coder generates a total of n bits of data, of which n − k {\displaystyle n-k} are redundant. If 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 codes) is ≤ R ⋅ k / n {\displaystyle \leq R\cdot k/n} . For example: The code rate of a convolutional code will typically be 1⁄2, 2⁄3, 3⁄4, 5⁄6, 7⁄8, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 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 codes. 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.

Non-redundant proportion of an error correction code data stream

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In telecommunication and information theory, the code rate (or information rate^[1]) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant). That is, if the code rate is k / n {\displaystyle k/n} , for every k bits of useful information, the coder generates a total of n bits of data, of which n − k {\displaystyle n-k} are redundant.

If 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 codes) is ≤ R ⋅ k / n {\displaystyle \leq R\cdot k/n} .

For example: The code rate of a convolutional code will typically be 1⁄2, 2⁄3, 3⁄4, 5⁄6, 7⁄8, etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the octet oriented Reed Solomon block code denoted RS(204,188) is 188/204, meaning that 204 − 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 codes.

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

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• Entropy rate
• Information rate
• Punctured code

References

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1. ^ Huffman, W. Cary, and Pless, Vera, Fundamentals of Error-Correcting Codes, Cambridge, 2003.

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