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It is shown here that the percolation cluster that emerges from thepercolation process on infinite perfect binary trees, is genuinely an encodingscheme for an infinite set of symbols. The average codeword length and theentropy of such an encoding scheme are still finite as long as the percolationdensity $p$ is between $1/2\leq p < \sqrt[3]{1/4}$.

Encoding Scheme for Infinite Set of Symbols: The Percolation Process on Infinite Perfect Binary Trees