A broad class of approaches to data compression that do not produce an exact copy of the original data when the data is uncompressed. Lossy compression is useful primarily in graphics and sound applications, where a certain loss of accuracy is acceptable in exchange for greater compression ratios, provided the degradation is carefully managed.

The engine behind data compression methods based on minimum redundancy coding. This chapter worked with an order-0 model, which simply determines the probability of any one symbol occurring in the data. Higher-order models look at the probabilities associated with combinations of symbols to get a more accurate determination of the data’s entropy. For example, if we encounter the symbol “Q” in text data, in many languages the probability is high that the next symbol will be “U.” Higher-order models take considerations like this into account.

The first form of minimum redundancy coding. Interestingly, it came about in the 1940s, apart from computers, as a result of experiments in information theory during World War II. Shannon-Fano coding is similar to Huffman coding, but it builds its tree from the top down instead of the bottom up.

A variation of Huffman coding that does not require that the table of frequencies be passed along with the compressed data. Instead, a statistical model is adapted as the data is compressed and uncompressed. The main benefit of adaptive Huffman coding is in using statistical models greater than the order-0 model described earlier. An order-0 model does not require much space, but the substantial space requirements of higher-order models make prepending a table impractical.

A popular method of data compression that addresses the inaccuracies in Huffman coding brought about by entropies that are fractional values of bits. Arithmetic coding avoids this by encoding data as a single, very long floating-point value that can be uniquely decoded.

Variations of LZ77 that use more effective methods than a sliding window to keep track of previously seen phrases. Generally, each method uses some type of data structure for efficient searching, such as a hash table (Chapter 8), a binary tree (see Chapter 9), or a trie (see the related topics at the end of Chapter 9), and applies some unique approach to optimizing the process of encoding and decoding phrases.