Overview
Range Coding is an arithmetic-coding variant that maintains a low value and range width while emitting bytes as the interval stabilizes.
SpecializedSource checked
Range Coding
Compresses symbols by narrowing a numeric range according to their probabilities.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Compression
- Difficulty
- Advanced
- Family
- Entropy Coding
- Tier
- Specialized
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 1
- Relationships
- 4
- Code example
- Ready
- Visualization
- Ready
Core Concepts
probability intervalcumulative modelrenormalizationentropy coding
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n)
Space
O(k)
When to Use
- Use when probability estimates are available and fractional-bit coding matters.
- Use when entropy coding in compressors is a central requirement.
When Not to Use
- Avoid when fixed prefix codes are good enough and simpler.
- Avoid when the added bit-level complexity is not worth the expected size reduction.
What It Does
- Maintains a coding interval
- Narrows the interval per symbol
- Emits stable leading bits or bytes
Use Cases
- Entropy coding in compressors
- Adaptive statistical coding
- Compact binary formats
Inputs
- Symbol stream
- Cumulative probability model
Outputs
- Compressed bitstream
Key Formulas (1)
Range update
rangenext = range · probability(symbol)
range_next = range * probability(symbol)Shrinks the current interval in proportion to the symbol probability.
Pseudocode
- 1.Start with a full numeric range
- 2.Look up the symbol's cumulative interval
- 3.Narrow low and range to that interval
- 4.Emit stable high-order bytes
- 5.Repeat until all symbols are encoded
Canonical Example
- Input
- model = A:0.75, B:0.25, input = A B
- Output
- range = narrowed first to A range then B subrange
- Explanation
- The final interval identifies the whole message.
Implementation Notes
- Use integer arithmetic and tests that compare encoder and decoder after every symbol.
- Write round-trip tests that encode and decode small hand-checked inputs.
- Keep a tiny example with expected output beside the implementation.
Common Pitfalls
- Off-by-one interval boundaries can make the decoder diverge after many symbols.
- Encoder and decoder must make exactly the same modeling and bit-order choices.
- Not defining boundary, empty, or degenerate inputs before implementation.
Interactive Mechanism Walkthrough
Sequence Window & Automaton AlignmentShow the active interval shrinking inside a probability range for each symbol.
Input:ABABABCABAB
Window:ABAB
Step 1 of 5: Start with a full numeric range
encoding-streamNotes
Finite-precision renormalization is the main implementation detail.
Sources (1)
What each reference supports for this entry.
Data Compression: The Complete Reference
BookCompression reference for range coding as an arithmetic-coding variant with integer interval updates.
Explore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toANS Coding
Both are entropy coding approaches used in modern compressors.
Variant ofArithmetic Coding
Range coding is a practical coding method closely related to arithmetic coding.
Related Algorithms
Tags
CompressionEntropy CodingEncoding