Abstract
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 information . It is essential that the law of 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 . 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fano, R.M.: Transmission of Information: A Statistical Theory of Communications, 1st edn. MIT Press, Cambridge (1961)
Fano, R.M.: Transmission of Information: A Statistical Theory of Communications (Translation to Russian). Mir, Moscow (1965)
Feinstein, A.: Foundations of Information Theory. McGraw-Hill, New York (1958)
Feinstein, A.: Foundations of Information Theory (Translation to Russian). Inostrannaya Literatura, Moscow (1960)
Huffman, D.A.: A method for the construction of minimum redundancy codes. Proc. IRE 40(9), 1098–1101 (1952)
Kraft, L.G.: A device for quantizing, grouping, and coding amplitude-modulated pulses. Master’s Thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering (1949)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Belavkin, R.V., Pardalos, P.M., Principe, J.C., Stratonovich, R.L. (2020). Encoding of discrete information in the absence of noise and penalties. In: Belavkin, R., Pardalos, P., Principe, J. (eds) Theory of Information and its Value. Springer, Cham. https://doi.org/10.1007/978-3-030-22833-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-22833-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-22832-3
Online ISBN: 978-3-030-22833-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)