Encoding of discrete information in the absence of noise and penalties

The definition of the amount of information, given in Chapter 1 , is justified when we deal with a transformation of information from one kind into another, i.e. when considering encoding of informationencoding of information . It is essential that the law of conservation of information amount law conservation of information amount holds under such a transformation. It is very useful to draw an analogy with the law of conservation of energy. The latter is the main argument for introducing the notion of energy. Of course, the law of conservation of information is more complex than the law of conservation of energy in two respects. The law of conservation of energy establishes an exact equality of energies, when one type of energy is transformed into another. However, in transforming information we have a more complex relation, namely ‘not greater’ ( ⩽ $$\leqslant $$ ), i.e. the amount of information cannot increase. The equality sign corresponds to optimal encoding encoding of information optimal . Thus, when formulating the law of conservation of information, we have to point out that there possibly exists such an encoding, for which the equality of the amounts of information occurs.