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Redundancy in information theory is the number of bits used to transmit a message minus the number of bits of actual information in the message. Informally, it is the amount of wasted "space" used to transmit certain data. Data compression is a way to reduce or eliminate unwanted redundancy, while checksums are a way of adding desired redundancy for purposes of error detection when communicating over a noisy channel of limited capacity. In describing the redundancy of raw data, recall that the rate of a source of information is the average entropy per symbol. For memoryless sources, this is merely the entropy of each symbol, while, in the most general case of a stochastic process, it is the limit, as n goes to infinity, of the joint entropy of the first n symbols divided by n. It is common in information theory to speak of the "rate" or "entropy" of a language. This is appropriate, for example, when the source of information is English prose. The rate of a memoryless source is simply H(M), since by definition there is no interdependence of the successive messages of a memoryless source. The absolute rate of a language or source is simply
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