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Everything about Arithmetic coding

Form of entropy encoding used in data compression

Arithmetic coding (AC) is a form of entropy coding used in lossless data compression. Normally, a string of characters is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and less-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding, in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, an arbitrary-precision fraction q, where 0.0 ≤ q < 1.0. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Arithmetic codingA 5-minute orientation
  2. Skim a recent paper: DNA-Aeon provides flexible arithmetic coding for constraint adherence and error correction in DNA storageInfluential work since 2022
  3. Pick up a classic book: Algebraic geometry codesThe most-reprinted book on the subject
  4. Read the landmark paper: Arithmetic coding for data compressionCited 2,051 times
  5. Go sideways: Asymmetric numeral systemsA closely related topic
  6. Go sideways: Range codingA closely related topic

đź“– Definitions

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🗂️ The subject at a glance

  1. Relationship to entropy
  2. Implementation details and examples
  3. Adaptive arithmetic coding
  4. Precision and renormalization
  5. Arithmetic coding as a generalized change of radix
  6. Connections with other compression methods
  7. History and patents
  8. Benchmarks and other technical characteristics

🏆 Landmark papers (most cited)

🆕 Influential since 2022

đź“š Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

đź”— Related topics