Code rate

Different code rates (Hamming code).

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 $k/n$ for every $k$ bits of useful information, the coder generates a total of $n$ bits of data, of which $n-k$ are redundant.

If $R$ is the gross bitrate or data signalling rate (inclusive of redundant error coding), the net bitrate (the useful bit rate exclusive of error-correction codes) is $\leq R\cdot k/n$ .

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.

References

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

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

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Code rate

See also

References