Average Codeword Length Calculator
Calculate the average length of codewords for efficient data compression and information theory analysis
Symbols and Probabilities
Calculation Options
Calculation Results
Enter your symbol probabilities and codeword lengths to analyze coding efficiency.
Detailed Breakdown
Your detailed codeword analysis will appear here.
📊 Codeword Assignment
| Symbol | Probability | Codeword Length | Codeword | Contribution |
|---|---|---|---|---|
| Add symbols to see codeword assignments | ||||
📚 Information Theory Basics
Average Codeword Length
L = Σ(pᵢ × lᵢ), where pᵢ is probability of symbol i and lᵢ is its codeword length. Represents the expected bits per symbol.
Entropy (H)
H = -Σ(pᵢ × log₂pᵢ). The theoretical minimum average bits needed to represent each symbol.
Efficiency
η = (H / L) × 100%. Measures how close the coding is to the theoretical limit.
Fixed-Length Coding
All symbols use the same number of bits. Simple but often inefficient for skewed distributions.
Variable-Length Coding
More probable symbols get shorter codewords. Can achieve better efficiency (e.g., Huffman coding).
Kraft's Inequality
Σ(2⁻ˡⁱ) ≤ 1 for uniquely decodable codes. Ensures codewords can be unambiguously decoded.
Note: This calculator provides information theory analysis for educational purposes. Actual compression performance may vary based on implementation details.