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 {displaystyle k} bits of useful information, the coder generates a total of n {displaystyle n} bits of data, of which n − k {displaystyle n-k} are redundant. 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 {displaystyle k} bits of useful information, the coder generates a total of n {displaystyle n} bits of data, of which n − k {displaystyle n-k} are redundant. If R {displaystyle 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 {displaystyle leq Rcdot k/n} . For example: The code rate of a convolutional code will typically be 1 / 2 {displaystyle 1/2} , 2 / 3 {displaystyle 2/3} , 3 / 4 {displaystyle 3/4} , 5 / 6 {displaystyle 5/6} , 7 / 8 {displaystyle 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 {displaystyle 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.