Shannon´s Source Code Theorem
The Source Coding Theorem, also known as Shannon's Source Coding Theorem, is a fundamental concept in information theory introduced by Claude Shannon in 1948. The theorem states that it is possible to compress data without loss of information, and that the amount of compression achievable is limited by the entropy of the source.
In mathematical terms, the theorem states that if a source produces symbols with probabilities p1, p2, ..., pn, then the average number of bits per symbol required to losslessly encode the data approaches the entropy of the source H(p), defined as H(p) = -Σ(pi log2 pi).
Shannon's Source Coding Theorem is important because it sets the theoretical limits for data compression and provides a basis for designing efficient data compression algorithms. The theorem is widely used in various fields, such as communication engineering, computer science, and data storage.
It's also worth noting that the theorem only applies to lossless data compression, meaning that the decompressed data should be exactly the same as the original data. There is another theorem, the Rate-Distortion theorem, which considers the trade-off between compression and the quality of the reconstructed data in lossy compression.
Low Probability Event - High Information Content
High Probability Event - Low Information Content
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