The capacity of a noisy channel is defined to be the maximum value of the mutual information of the input and output variables with respect to the probability distribution over the input alphabets.

Claude Shannon's noisy channel coding theorem states that an error correcting code exists such that it is possible to communicate over a noisy channel at a rate equal to or lower than the capacity with an arbitarily small probability of bit error.

Ca*pac"i*ty (?), n.; pl. Capacities (#) [L. capacitus, fr. capax, capacis; fr. F. capacit'e. See Capacious.]

1.

The power of receiving or containing; extent of room or space; passive power; -- used in reference to physical things.

Had our great palace the capacity To camp this host, we all would sup together. Shak.

The capacity of the exhausted cylinder. Boyle.

2.

The power of receiving and holding ideas, knowledge, etc.; the comprehensiveness of the mind; the receptive faculty; capability of undestanding or feeling.

Capacity is now properly limited to these [the mere passive operations of the mind]; its primary signification, which is literally room for, as well as its employment, favars this; although it can not be dented that there are examples of its usage in an active sense. Sir W. Hamilton.

3.

Ability; power pertaining to, or resulting from, the possession of strength, wealth, or talent; possibility of being or of doing.

The capacity of blessing the people. Alex. Hamilton.

A cause with such capacities endued. Blackmore.

4.

Outward condition or circumstances; occupation; profession; character; position; as, to work in the capacity of a mason or a carpenter.

5. Law

Legal or noral qualification, as of age, residence, character, etc., necessary for certain purposes, as for holding office, for marrying, for making contracts, will, etc.; legal power or right; competency.

Capacity for heat, the power of absorbing heat. Substances differ in the amount of heat requisite to raise them a given number of thermometric degrees, and this difference is the measure of, or depends upon, whzt is called their capacity for heat. See Specific heat, under Heat.

Syn. -- Ability; faculty; talent; capability; skill; efficiency; cleverness. See Ability.