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// Arithmetic Coding - Fractional bit encoding approaching entropy limit
Near-Optimal
Approaches theoretical entropy limit for compression efficiency.
Fractional Bits
Encodes symbols using fractional bits based on probability.
Streamable
Can encode and decode data incrementally as it arrives.
>> technical info
How Arithmetic Coding Works:
Arithmetic coding represents an entire message as a single number in the interval [0,1). Each symbol narrows this interval based on its probability. The final interval is encoded as a binary fraction, achieving compression very close to the entropy limit.
Encoding Process:
Text: "AAB" Probabilities: A=0.67, B=0.33 1. Start: [0, 1) 2. 'A': [0, 0.67) 3. 'A': [0, 0.45) 4. 'B': [0.30, 0.45) Output: Any number in [0.30, 0.45) Binary: 0.010011...
Why Use Arithmetic Coding:
- >Best compression ratios
- >Approaches entropy limit
- >Handles any probability
- >Used in JPEG2000/H.264
- >Patent-expired (2024)
>> frequently asked questions
What is arithmetic coding?
Arithmetic coding is a form of entropy encoding that converts a sequence of symbols into a single fractional number. Unlike Huffman coding which uses whole bits, arithmetic coding can use fractional bits per symbol.
Why is it better than Huffman?
Arithmetic coding can achieve compression arbitrarily close to the entropy limit, while Huffman is limited to whole bits per symbol. For highly skewed probabilities, arithmetic coding can be significantly better.
What's the precision parameter?
Precision controls the number of bits used for internal calculations. Higher precision allows encoding longer messages but requires more memory. 16-bit is usually sufficient for short texts.
Where is arithmetic coding used?
Arithmetic coding is used in modern compression standards like H.264/H.265 video, JPEG2000 images, and ZIP's DEFLATE64. It was previously patent-encumbered but key patents expired.