LYCOS RETRIEVER 
Entropy Encoding: Symbols
built 200 days ago
Arithmetic coding is a technique for achieving near-optimal entropy encoding. An arithmetic encoder takes a string of symbols as input and produces a rational number in the interval, as output. As each symbol is processed, the encoder will restrict the output to a smaller interval. represent the probability of each symbol appearing. . Note that at each stage, all the possible intervals are pairwise disjoint. Therefore a specific sequence of symbols produces exactly one unique output range, and the process can be reversed.
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The block codes from the DPCM and run-length models can be further compressed using entropy encoding. For the baseline JPEG method, the Huffman coder is used to reduce entropy. One reason for using the Huffman coder is that it is easy to implement by means of a lookup table in hardware. To compress data symbols, the Huffman coder creates shorter codes for frequently occurring symbols and longer codes for occasionally occurring symbols. Many applications may use predefined Huffman tables. Therefore, the baseline encoder can operate as a one-pass or two-pass system.
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Arithmetic encoding is a form of near-optimal entropy encoding. It takes a string of symbols as input and produces a binary string as output. For this project, a table of the probability of each number occurring in the signal was given to the arithmetic encoder along with the signal to be compressed. As Arithmetic encoding requires natural integers, the data was shifted up beforehand, making the lowest number equal to 1.
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In entropy, e.g. arithmetic, encoding and decoding, probability estimates are needed of symbols to be encoded and subsequently decoded. More accurate probability estimates are obtained by controllably adjusting the adaptation rate of an adaptive probability estimator. The adaptation rate is optimized by matching it to the actual probability values being estimated. In particular, the adaptation rate is optimized to be proportional to the inverse of the smallest value probability being estimated. Consequently, if the probability values being estimated are not small a "fast" adaption rate is realized and if the probability values being estimated are small a necessarily slower adaptation rate is realized.
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An entropy encoding is a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols. Typically, entropy encoders are used to compress data by replacing symbols represented by equal-length codes with symbols represented by codes where the length of each codeword is proportional to the negative logarithm of the probability. Therefore, the most common symbols use the shortest codes.
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