Set Shaping Theory

Set Shaping Theory (information theory)

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The Set Shaping Theory has as its objective the study of bijection functions that transform a set of strings into a set of equal size made up of strings of greater length. The functions that respect this condition are many but, since the purpose of this theory is the transmission of data, the most studied function is the one that minimizes the average information content.

Applying this type of function, we obtain an unexpected result in which we observe that the lower information content of the string compensates for its greater length. Furthermore, this compensation is not constant but depends on the typical set. In practice, we observe a very interesting phenomenon in which the gain or loss in terms of compression changes according to the characteristics of the source.

Bibliography

1. Kozlov, Solomon. "Introduction to Set Shaping Theory." arXiv preprint arXiv:2111.08369 (2021).

2. Cover, Thomas M. (2006). Elements of Information Theory. John Wiley & Sons. ISBN 0-471-24195-4.