On the random property of compressed data via Huffman coding

Though Huffman codes [2,3,4,5,9] have shown their power in data compression, there are still some issues that are not noticed. In the present paper, we address the issue on the random property of compressed data via Huffman coding. Randomized computation is the only known method for many notoriously difficult #P-complete problems such as permanent, and some network reliability problems, etc [1,7,8,10]. According to Kolmogorov complexity [6,10], a truly random binary string is very difficult to compress and for any fixed length there exist incompressible strings. In other words, incompressible strings tend to carry higher degree of randomness. We study this phenomenon via Huffman coding. We take compressed data as random source that provides coin flips for randomized algorithms. A simple randomized algorithm is proposed to calculate the value of πwith the compressed data as random number. Experimental results show that compressed data via Huffman coding does provide a better approximation for calculating π, especially in the first few round of the compressions. We try several different types of files and obtain similar results that compressed data is random for the testing example. Keyword: data compression, Huffman coding, random number generator, randomized algorithms, Kolmogorov complexity