Huffman Coding

Huffman coding is a popular method for compressing data with variable-length codes. Given a set of data symbols (an alphabet) and their frequencies of occurrence (or, equivalently, their probabilities), the method constructs a set of variable-length codewords with the shortest average length and assigns them to the symbols. Huffman coding serves as the basis for several applications implemented on popular platforms. Some programs use just the Huffman method, while others use it as one step in a multistep compression process. The Huffman method [Huffman 52] is somewhat similar to the Shannon—Fano method, proposed independently by Claude Shannon and Robert Fano in the late 1940s ([Shannon 48] and [Fano 49]). It generally produces better codes, and like the Shannon—Fano method, it produces the best variable-length codes when the probabilities of the symbols are negative powers of 2. The main difference between the two methods is that Shannon—Fano constructs its codes from top to bottom (and the bits of each codeword are constructed from left to right), while Huffman constructs a code tree from the bottom up (and the bits of each codeword are constructed from right to left).