> shannon | fano | entropy <
// Shannon-Fano - Top-down entropy encoding for data compression
Entropy-Based
Uses information theory to create efficient variable-length codes.
Top-Down Approach
Recursively divides symbols into groups of similar probability.
Historical Algorithm
Pioneering method that influenced modern compression techniques.
>> technical info
How Shannon-Fano Works:
Shannon-Fano coding sorts symbols by frequency, then recursively divides them into two groups with approximately equal probability. Each split adds a bit to the code (0 for left, 1 for right). The result is a prefix-free variable-length code.
Encoding Process:
Text: "AAABBCD" Frequencies: A:3, B:2, C:1, D:1 Split: [A] | [B,C,D] Codes: A: 0 B: 10 C: 110 D: 111 Encoded: 0 0 0 10 10 110 111
Why Use Shannon-Fano:
- >Simple to implement
- >Good compression ratios
- >Historical significance
- >Educational value
- >Prefix-free codes
>> frequently asked questions
What is Shannon-Fano coding?
Shannon-Fano coding is an entropy encoding technique developed by Claude Shannon and Robert Fano in the 1940s. It was one of the first algorithms to use variable-length codes based on symbol probabilities.
Shannon-Fano vs Huffman?
Both create variable-length codes, but Huffman is optimal (produces the shortest average code length). Shannon-Fano is simpler but may produce slightly longer codes. Huffman builds bottom-up, Shannon-Fano top-down.
How does the splitting work?
Symbols are sorted by frequency, then divided into two groups with probabilities as close as possible. This process repeats recursively for each group until each contains only one symbol.
Is Shannon-Fano still used?
Shannon-Fano is mainly of historical interest now. Huffman coding replaced it for most applications due to guaranteed optimality. However, Shannon-Fano remains valuable for teaching compression concepts.