Shannon's source coding theorem

In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the statistical limits to possible data compression for data whose source is an independent identically-distributed random variable, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that, in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity, it is impossible to compress such data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost.

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