Huffman Coding - Main Properties

Main Properties

The probabilities used can be generic ones for the application domain that are based on average experience, or they can be the actual frequencies found in the text being compressed. (This variation requires that a frequency table or other hint as to the encoding must be stored with the compressed text; implementations employ various tricks to store tables efficiently.)

Huffman coding is optimal when the probability of each input symbol is a negative power of two. Prefix codes tend to have inefficiency on small alphabets, where probabilities often fall between these optimal points. "Blocking", or expanding the alphabet size by grouping multiple symbols into "words" of fixed or variable-length before Huffman coding helps both to reduce that inefficiency and to take advantage of statistical dependencies between input symbols within the group (as in the case of natural language text). The worst case for Huffman coding can happen when the probability of a symbol exceeds 2−1 = 0.5, making the upper limit of inefficiency unbounded. These situations often respond well to a form of blocking called run-length encoding; for the simple case of Bernoulli processes, Golomb coding is a provably optimal run-length code.

Arithmetic coding produces some gains over Huffman coding, although arithmetic coding has higher computational complexity. Also, arithmetic coding was historically a subject of some concern over patent issues. However, as of mid-2010, various well-known effective techniques for arithmetic coding have passed into the public domain as the early patents have expired.