telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...

and

information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

, the code rate (or information rateHuffman, W. Cary, and Pless, Vera, ''Fundamentals of Error-Correcting Codes'', Cambridge, 2003.) of a

forward error correction In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

code is the proportion of the data-stream that is useful (non- redundant). That is, if the code rate is

k/n

for every bits of useful information, the coder generates a total of bits of data, of which

n-k

are redundant. If is the

gross bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...

data signalling rate In telecommunication, data signaling rate (DSR), also known as gross bit rate, is the aggregate rate at which data passes a point in the transmission path of a data transmission system. # The DSR is usually expressed in bits per second. # The d ...

(inclusive of redundant error coding), the

net bit rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...

(the useful bit rate exclusive of

error correction code In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

s) is

\leq R \cdot k/n

. For example: The code rate of a

convolutional code In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of t ...

will typically be , , , , , etc., corresponding to one redundant bit inserted after every single, second, third, etc., bit. The code rate of the

octet Octet may refer to: Music * Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble ** String octet, a piece of music written for eight string instruments *** Octet (Mendelssohn), 1825 compos ...

oriented

Reed Solomon Reed or Reeds may refer to: Science, technology, biology, and medicine * Reed bird (disambiguation) * Reed pen, writing implement in use since ancient times * Reed (plant), one of several tall, grass-like wetland plants of the order Poales * Re ...

block code In coding theory, block codes are a 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. The abstract defini ...

denoted RS(204,188) is 188/204, meaning that 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 code In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence of encoding symbols can be generated from a given set of source symbols such that the origi ...

s. Note that

bit/s In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...

is a more widespread

unit of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...

for the

information rate In telecommunications and computing, bit rate (bitrate or as a variable ''R'') is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed in the unit bit per second (symbol: bit/s), often in conjunction w ...

, implying that it is synonymous with ''net bit rate'' or ''useful bit rate'' exclusive of error-correction codes.

References

Information theory Rates {{Comp-sci-stub

See also

References