Practical applications of Set Shaping Theory in Huffman coding

Abstract: One of the biggest criticisms of the Set Shaping Theory is the lack of a practical application. This is due to the difficulty of its application. In fact, to apply this technique from an experimental point of view we must use a table that defines the correspondences between two sets. However, this approach is not usable in practice, because the table has A^N elements, with A number of symbols and N length of the message to be encoded. Consequently, these tables can be implemented in a program only when A and N have a low value. Unfortunately, in these cases, there are no compression algorithms with such efficiency as to detect the improvement introduced by this method. In this article, we use a function capable of performing the transform without using the correspondence table; this allows us to apply this theory to a wide range of values of A and N. The results obtained confirm the theoretical predictions.