Performance of Lempel-Ziv compressors with deferred innovation

The noiseless data-compression algorithms introduced by Lempel and Ziv (LZ) parse an input data string into successive substrings each consisting of two parts: The citation, which is the longest prefix that has appeared earlier in the input, and the innovation, which is the symbol immediately following the citation. In extremal versions of the LZ algorithm the citation may have begun anywhere in the input; in incremental versions it must have begun at a previous parse position. Originally the citation and the innovation were encoded, either individually or jointly, into an output word to be transmitted or stored. Subsequently, it was speculated that the cost of this encoding may be excessively high because the innovation contributes roughly 1g(A) bits, where A is the size of the input alphabet, regardless of the compressibility of the source. To remedy this excess, it was suggested to store the parsed substring as usual, but encoding for output only the citation, leaving the innovation to be encoded as the first symbol of the next substring. Being thus included in the next substring, the innovation can participate in whatever compression that substring enjoys. This strategy is called deferred innovation. It is exemplified in the algorithm described by Welch and implemented in the C program compress that has widely displaced adaptive Huffman coding (compact) as a UNIX system utility. The excessive expansion is explained, an implicit warning is given against using the deferred innovation compressors on nearly incompressible data.