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Questions tagged [lempel-ziv]

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Lempel-Zilv-Welch Algorithm Decoding Question

Hello i am studying about LZW algorithm by watching this video: https://www.youtube.com/watch?v=j2HSd3HCpDs&t=481s I couldnt fully understand decoding process. At current 258,how does 116 come at ...
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2answers
5k views

Huffman Coding vs LZW Algorithm

I'm trying to understand comparisons between the two. Is there ever a case where is it better to use Huffman Coding over LZW? Could the compression ratio for Huffman ever surpass that of LZW? Thanks!...
5
votes
0answers
295 views

LZ-type compression with a limited recursion depth

I would like to begin by apologizing. I am not a computer scientist, so my use of terminology will be off. I came across an interesting problem, which I believe to be pretty hard and would love to get ...
1
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1answer
88 views

Number of phrases of LZ compression

It is known that for the number $c(n)$ of phrases / tupel of the LZ compression for binary words of length $n$ the following relation holds: $$c(n)\leq\frac{n}{(1-\epsilon_n)\log_2 n}$$ With $\...
2
votes
1answer
838 views

LZW decoding process

I'm trying to understand how LZW decodes a string. For example suppose that we have a dictionary where: a=0 b=1 and we have to encode the string "aabbabaabb", so the output of the encoding process (...
2
votes
2answers
554 views

How optimal is Lempel-Ziv at reaching the Shannon limit?

I find this a bit difficult to describe, but I am interested in the following idea : The LZ algorithm factors (verb) an input stream into adjacent factors, these are by definition the maximal ...
6
votes
2answers
183 views

Behavior of iterative application of LZ77

I have been experimenting with LZ77 (naively $O(n^2)$ runtime, infinite window). Applying it to the 7th Fibonacci word $abaababaabaab$ yields the correct LZ factorization: $\qquad a,b,a,aba,baaba,ab$....