Code rate

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 totally 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 ≤ R•k/n.

For example: The code rate of a convolutional code may typically be 1/2, 2/3, 3/4, 5/6, 7/8, etc, corresponding to that one redundant bit is inserted after every single, second, third, etc, bit. The code rate of the Reed Solomon block code denoted RS(204,188) is 188/204, corresponding to that 204 - 188 = 16 redundant bytes are added to each block of 188 byte 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 to net bit rate or useful bit rate exclusive of error-correction codes.

See also

• Information rate
• Source information rate (Entropy rate)

References

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