In information theory, an entropy coding (or entropy encoding) is a lossless data compression scheme that is independent of the specific characteristics of the medium.

One of the main types of entropy coding creates and assigns a unique prefix-free code to each unique symbol that occurs in the input. [1] These entropy encoders then compress data by replacing each fixed-length input symbol with the corresponding variable-length prefix-free output codeword. The length of each codeword is approximately proportional to the negative logarithm of the probability of occurrence of that codeword. Therefore, the most common symbols use the shortest codes.[2]

According to Shannon's source coding theorem, the optimal code length for a symbol is ${\displaystyle -log_{b}(P)}$, where ${\displaystyle b}$ is the number of symbols used to make output codes and ${\displaystyle P}$ is the probability of the input symbol.

Two of the most common entropy coding techniques are Huffman coding and arithmetic coding.[3] If the approximate entropy characteristics of a data stream are known in advance (especially for signal compression), a simpler static code may be useful. These static codes include universal codes (such as Elias gamma coding or Fibonacci coding) and Golomb codes (such as unary coding or Rice coding).

Since 2014, data compressors have started using the Asymmetric Numeral Systems family of entropy coding techniques, which allows combination of the compression ratio of arithmetic coding with a processing cost similar to Huffman coding.

## Entropy as a measure of similarity

Besides using entropy coding as a way to compress digital data, an entropy encoder can also be used to measure the amount of similarity between streams of data and already existing classes of data. This is done by generating an entropy coder/compressor for each class of data; unknown data is then classified by feeding the uncompressed data to each compressor and seeing which compressor yields the highest compression. The coder with the best compression is probably the coder trained on the data that was most similar to the unknown data.