Code: Difference between revisions

Revision as of 12:36, 11 April 2025

Revision as of 06:01, 22 April 2025

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In this section, we consider codes that encode each source (clear text) character by a [[Code word (figure of speech)|code word]] from some dictionary, and [[concatenation]] of such code words give us an encoded string. Variable-length codes are especially useful when clear text characters have different probabilities; see also [[entropy encoding]].

A ''prefix code'' is a code with the "prefix property": there is no valid code word in the system that is a [[prefix (computer science)|prefix]] (start) of any other valid code word in the set. [[Huffman coding]] is the most known algorithm for deriving prefix codes. Prefix codes are widely referred to as "Huffman codes" even when the code was not produced by a Huffman algorithm. Other examples of prefix codes are [[countrytelephone callingcountry codes]], the country and publisher parts of [[ISBN]]s, and the Secondary Synchronization Codes used in the [[UMTS]] [[W-CDMA|WCDMA]] 3G Wireless Standard.

[[Kraft's inequality]] characterizes the sets of codeword lengths that are possible in a prefix code. Virtually any uniquely decodable one-to-many code, not necessarily a prefix one, must satisfy Kraft's inequality.