The codes from 0 to represent 1-character sequences consisting of the corresponding 8-bit character, and the codes through are created in a dictionary for sequences encountered in the data as it is encoded. At each stage in compression, input bytes are gathered into a sequence until the next character would make a sequence with no code yet in the dictionary. The code for the sequence without that character is added to the output, and a new code for the sequence with that character is added to the dictionary. The idea was quickly adapted to other situations.

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As you can see, the decoder comes across an index of 4 while the entry that belongs there is currently being processed. To understand why this happens, take a look at the encoding table. Immediately after "aba" with an index of 4 is entered into the dictionary, the next substring that is encoded is an "aba" ie.

Therefore the pseudocode provided above must be altered a bit in order to handle all cases. Remember that you must start with the same initial dictionary ie. To help yourself, make a decoding table like above. Data Structure. Both encoding and decoding programs refer to the dictionary countless times during the algorithm.

A data structure with 0 1 search complexity would be extremely handy. The encoder looks up indexes in the dictionary by using strings what structure might be good for this? In Huffman coding, a pseudo-eof is output at the end of the output so that the decoder will know when the end of encoded output has been reached. Although LZW generally does not require a pseudo-eof normally, it reads data until it can read no more , it is a good idea to use one.

Probably the easiest way to do this is to reserve a spot in the dictionary say, the last index for the pseudo-eof nothing actually gets stored there.

When you are finished encoding, just write the index of the pseudo-eof. Needless to say, the decoding program must also reserve that index to signal the pseudo-eof Flush Character. This too is an optional feature. When the uncompression program reads the index for the flush character, it will reset the dictionary to its intial state.

See, once the dictionary becomes full, it ceases to be dynamic, therefore ceasing to reflect local characteristics. Using the flush character, however, you could monitor the compression ratio and flush the dictionary whenever the ratio falls below a certain threshold. Toy around with this one, and you could have a pretty good compression program at your disposal.

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## La compression de données

Theoretical efficiency[ edit ] In the second of the two papers that introduced these algorithms they are analyzed as encoders defined by finite-state machines. A measure analogous to information entropy is developed for individual sequences as opposed to probabilistic ensembles. This measure gives a bound on the data compression ratio that can be achieved. It is then shown that there exist finite lossless encoders for every sequence that achieve this bound as the length of the sequence grows to infinity. In this sense an algorithm based on this scheme produces asymptotically optimal encodings. This result can be proven more directly, as for example in notes by Peter Shor. A match is encoded by a pair of numbers called a length-distance pair, which is equivalent to the statement "each of the next length characters is equal to the characters exactly distance characters behind it in the uncompressed stream".

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## ALGORITHME LZW PDF

As you can see, the decoder comes across an index of 4 while the entry that belongs there is currently being processed. To understand why this happens, take a look at the encoding table. Immediately after "aba" with an index of 4 is entered into the dictionary, the next substring that is encoded is an "aba" ie. Therefore the pseudocode provided above must be altered a bit in order to handle all cases. Remember that you must start with the same initial dictionary ie. To help yourself, make a decoding table like above.

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## Lempel–Ziv–Welch

Dictionary based algorithms scan a file for sequences of data that occur more than once. These sequences are then stored in a dictionary and within the compressed file, references are put where-ever repetitive data occurred. Lempel and Ziv published a series of papers describing various compression algorithms. Their first algorithm was published in , hence its name: LZ This compression algorithm maintains its dictionary within the data themselves.

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