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LZ77 and LZ78 are the two lossless data compression algorithms published in papers by Abraham Lempel and Jacob Ziv in 1977 [1] and 1978. [2] They are also known as Lempel-Ziv 1 (LZ1) and Lempel-Ziv 2 (LZ2) respectively. [3] These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others. Besides their academic ...
Together with F, this makes 2 N +1 files that all compress into one of the 2 N files of length N. But 2 N is smaller than 2 N +1, so by the pigeonhole principle there must be some file of length N that is simultaneously the output of the compression function on two different inputs. That file cannot be decompressed reliably (which of the two ...
bzip2 is a free and open-source file compression program that uses the Burrows–Wheeler algorithm.It only compresses single files and is not a file archiver.It relies on separate external utilities such as tar for tasks such as handling multiple files, and other tools for encryption, and archive splitting.
In information theory, data compression, source coding, [1] or bit-rate reduction is the process of encoding information using fewer bits than the original representation. [2] Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in ...
Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%. For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...