In search for the simplest example that proves Huffman coding overperforms Shannon-Fano coding

Abstract

Abstract Shannon-Fano coding (SFC) and Huffman coding (HC) are classic and well-known algorithms, but still in use today. The search for the simplest example that proves HC overperforms SFC is still of interest. The problem is not as trivial as it looks like at first view because of several decisions that must be considered. We perform a full-search of the stream data space for a maximum stream length of 100. Depending on additional requests we impose, the simplest solution we found is {1,1,1,1,3} when we accept to select a specific cutting, {2,3,3,3,7} when we accept only deterministic (unique) cuttings and {4,5,6,7,14} when we also ask for different frequencies for symbols as well.