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 $$k/n$$ 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 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 $$\leq R \cdot k/n$$.

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 $204 &minus; 188 = 16$ 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 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.