Code rate

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Different code rates (Hamming code)

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 .mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}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.

• Entropy rate
• Information rate
• Punctured code

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