Compression: How Can Fewer Symbols Preserve Information?

Compression does not mean shortening content by arbitrary deletion. It uses repetition and predictable relationships to express the original information with fewer symbols. A sequence containing the same character one hundred times, for example, can be recorded as “repeat this character one hundred times”. If sender and receiver share the rule, each occurrence need not be stored separately.

Lossless compression must reconstruct the original data, which matters for programs, accounts and other material that cannot tolerate alteration. Lossy compression instead specifies which differences may be discarded. A photograph may omit detail to which human vision is less sensitive in exchange for a smaller file. That is not inherently inferior; the question is whether the loss crosses the boundary set by the use. An image acceptable for ordinary viewing may be unsuitable for fingerprint examination.

Compression is related to summarising, but they are not the same. A summary normally selects what matters and does not promise to restore the original text. Compression is chiefly concerned with encoding, decoding and acceptable error. The concept matters because the amount of information is not simply the number of symbols. Whether a shorter form works reliably depends on the rules available to the receiver and on what must later be recovered.

https://ocw.mit.edu/courses/6-441-information-theory-spring-2016/pages/lecture-notes/
https://www.nist.gov/publications/parallel-algorithms-entropy-coding-techniques