Code rate
Encyclopedia
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 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.
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
and information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
, the code rate (or information rate) of a forward error correction
Forward error correction
In telecommunication, information theory, and coding theory, forward error correction or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels....
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
Convolutional code
In telecommunication, a convolutional code is a type of error-correcting code in which* each m-bit information symbol to be encoded is transformed into an n-bit symbol, where m/n is the code rate and...
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
Block code
In coding theory, block codes refers to the large and important family of error-correcting codes that encode data in blocks.There is a vast number of examples for block codes, many of which have a wide range of practical applications...
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.