Channel capacity is the best reliable information rate available through a specified communication channel. For a discrete memoryless channel with finite input and output alphabets, fixed transition probabilities , and no input-cost constraint, it isin bits per channel use, when the mutual information uses base-two logarithms. The maximization varies the input probability distribution, while keeping the communication channel fixed. A large input alphabet or a large output information entropy alone does not determine how much information gets through: the receiver needs information about the input, rather than merely unpredictable output.
The operational meaning comes from the Shannon second coding theorem. A block code represents one of possible messages by a word of length , giving a rate bits per use. Take the message label from the uniform distribution on a finite set of those choices when measuring average decoding-error probability. For every fixed rate , there are sequences of such block codes whose decoding-error probability tends to zero as grows; a rate above cannot have vanishing decoding-error probability. This is an asymptotic limit, rather than a promise that an arbitrary finite block code at a rate below works well. See MIT 18.310, Shannon's Noisy Coding Theorem, sections 1–2.
For a binary symmetric channel with crossover probability , the binary symmetric channel capacity is approximately bits per use. Thus a binary code rate lies below the limit, while lies above it. At , two transmitted symbols represent one message bit on average; the redundancy helps distinguish messages after noise. This does not split individual physical symbols into fractional pieces.
The result is useful because it separates two tasks. Computing channel capacity establishes the target imposed by the transition probabilities; constructing an effective block code attempts to approach that target with acceptable delay and decoding effort. The surprise is that reliability can improve indefinitely without forcing every positive rate to disappear. In his 1948 paper, Shannon defines noisy channel capacity in section 12 and develops its operational significance in section 13, Theorem 11. His original formulation uses information per unit time; the fixed-duration channel-use convention here expresses the same rate question per symbol. [ref].
Channel capacity is a fundamental concept in information theory that represents the maximum rate at which information can be reliably transmitted over a communication channel. More specifically, it refers to the highest data rate (measured in bits per second, bps) that can be achieved without significant errors as the length of transmission approaches infinity. The concept was introduced by Claude Shannon in his seminal 1948 paper "A Mathematical Theory of Communication.
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