Fountain Codes and Invertible Matrices

This paper deals with Fountain codes, and especially with their encoding matrices, which are required here to be invertible. A result is stated that an encoding matrix induces a permutation. Also, a result is that encoding matrices form a group with multiplication operation. An encoding is a transformation, which reduces the entropy of an initially high-entropy input vector. A special encoding matrix, with which the entropy reduction is more effective than with matrices created by the Ideal Soliton distribution is formed. Experimental results with entropy reduction are shown.