Shannonkildekoding

Shannonkildekoding is a term used in Danish-language contexts to denote Shannon's source coding theory, the portion of information theory that studies the efficient representation of information sources. It concerns how a stream of symbols produced by a source can be encoded with minimum average length while preserving information content, particularly in the lossless setting. In practice, the subject investigates how close an encoding can come to the source's intrinsic information content, measured by entropy, and what codes achieve that limit.

A central result is the source coding theorem: for any discrete memoryless source with entropy H(X), there exist codes with average length L that satisfies H(X) ≤ L < H(X) + 1 (for certain coding schemes) for sufficiently long block lengths. Conversely, no scheme can achieve an average length below H(X). This framework underpins the design of practical compression methods. Prefix codes, such as Huffman coding, and arithmetic coding are examples of schemes that approach the theoretical limit. The field also includes lossy source coding and rate-distortion theory, which relax exact reconstruction to allow controlled distortion.

Historically, Shannonkildekoding follows from Claude Shannon's 1948 A Mathematical Theory of Communication, which established entropy as a measure of information and laid the groundwork for data compression and reliable communication. Today, the concepts inform a wide range of applications, from file and image compression to digital transmission systems and streaming technologies.

See also: entropy, source coding theorem, rate-distortion theory, Huffman coding, arithmetic coding.