Fast Construction of Disposable Prefix-Free Codes

Some data compression techniques use large numbers of prefix-free codes. The following two techniques do so: adaptive Huffman encoding and bit recycling. Adaptive Huffman encoding allows successive symbols to be encoded where each one is encoded according to the statistics of the symbols seen so far. Bit recycling, on the other hand, is a technique that is designed to improve the efficiency of a certain class of compression techniques (that is, the ones that allow for the existence of multiple encodings of the same data) and that repetitively has to build prefix-free codes that are used to encode or decode only one symbol. In the case of adaptive Huffman encoding, the simple but inefficient solution consists in building a prefix-free code from scratch according to the current statistics (using, say, Huffman’s algorithm) before encoding each symbol. However, there exist efficient algorithms for adaptive encoding that take advantage of the fact that the statistics evolve only progressively (e.g., Vitter’s algorithm). Bit recycling, on the other hand, is unlikely to reuse the same, or even a similar, prefix-free code. Consequently, a lot of prefix-free codes need to be constructed from scratch. What we propose is to use a fast technique to construct prefix-free codes. The technique trades speed in exchange of the optimality of the prefix-free codes it builds. We measured that the technique is 3 to 4 times faster than Huffman’s algorithm, while the encodings of the symbols are only 4% or 1.4% longer on average, depending on whether the technique is used in a general context or in a bit-recycling one, respectively.