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Code rate

Non-redundant proportion of an error correction code data stream

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated February 27, 2026
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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 a total of n bits of data, of which 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 \leq R\cdot k/n.

For example: The code rate of a convolutional code will typically be 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.

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This article is adapted from the Wikipedia article “Code rate”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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Entropy rate

In the mathematical theory of probability, the entropy rate or source information rate of a stochastic process is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate H {\displaystyle H(X)} is the limit of the joint entropy of n {\displaystyle n} members of the process X k {\displaystyle X_{k}} divided by n {\displaystyle n} , as n {\displaystyle n} tends to infinity: H ( X ) = lim n → ∞ 1 n H ( X 1 , X 2 , … X n ) {\displaystyle H(X)=\lim _{n\to \infty }{\frac {1}{n}}H(X_{1},X_{2},\dots X_{n})} when the limit exists.

Bit rate

In telecommunications and computing, bit rate is the number of bits that are conveyed or processed per unit of time. The bit rate is expressed as bits per second (symbol: bit/s), often with an SI prefix such as kilo (1 kbit/s = 1,000 bit/s), mega (1 Mbit/s = 1,000 kbit/s), giga (1 Gbit/s = 1,000 Mbit/s) or tera (1 Tbit/s = 1,000 Gbit/s).

Punctured code

In coding theory, puncturing is the process of removing some of the parity bits after encoding with an error-correction code. This has the same effect as encoding with an error-correction code with a higher rate, or less redundancy.