Channel capacity, in electrical engineering, computer science, and information theory, is the tight upper bound on the rate at which information can be reliably transmitted over a communication channel.
Following the terms of the noisy-channel coding theorem, the channel capacity of a given channel is the highest information rate (in units of information per unit time) that can be achieved with arbitrarily small error probability.
Information theory, developed by Claude E. Shannon in 1948, defines the notion of channel capacity and provides a mathematical model by which it may be computed. The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution.
The notion of channel capacity has been central to the development of modern wireline and wireless communication systems, with the advent of novel error correction coding mechanisms that have resulted in achieving performance very close to the limits promised by channel capacity.
The basic mathematical model for a communication system is the following:
where:
is the message to be transmitted;
is the channel input symbol ( is a sequence of symbols) taken in an alphabet ;
is the channel output symbol ( is a sequence of symbols) taken in an alphabet ;
is the estimate of the transmitted message;
is the encoding function for a block of length ;
is the noisy channel, which is modeled by a conditional probability distribution; and,
is the decoding function for a block of length .
Let and be modeled as random variables. Furthermore, let be the conditional probability distribution function of given , which is an inherent fixed property of the communication channel. Then the choice of the marginal distribution completely determines the joint distribution due to the identity
which, in turn, induces a mutual information . The channel capacity is defined as
where the supremum is taken over all possible choices of .
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In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels. The central idea is that the sender encodes the message in a redundant way, most often by using an error correction code or error correcting code (ECC). The redundancy allows the receiver not only to detect errors that may occur anywhere in the message, but often to correct a limited number of errors.
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 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). The non-standard abbreviation bps is often used to replace the standard symbol bit/s, so that, for example, 1 Mbps is used to mean one million bits per second.
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level, information pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information. Whereas digital signals and other data use discrete signs to convey information, other phenomena and artefacts such as analogue signals, poems, pictures, music or other sounds, and currents convey information in a more continuous form.
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