Fast gapped variants for Lempel--Ziv--Welch compression
Information and Computation
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We propose new algorithms, collectively termed, codelet parsing, for lossycompression.The algorithms sequentially parse a given source sequence intophrases, say, sourcelets, and map each sourcelet to a distorted phrase, say, acodelet, such that the per-letter distortion between the two phrases does notexceed the desired distortion.The algorithms adaptively maintain a codebook(a set of codewords), and do not require any a priori knowledge of the sorucestatistics.The algorithms use approximate string matching and, as key newidea, at each epoch, carefully select one of the many approximately matchingcodewords to balance between the code rate in the current epoch versus the coderate from resulting codebooks in future epochs.The algorithms are quadratic-timein the length of the source sequence and output a distorted sequence thatcan be naturally losslessly compressed using the Lempel-Ziv (LZ78) algorithm.