Główne pojęcia
A prefix code is optimal if and only if it is complete and strongly monotone.
Streszczenie
The paper introduces a new property called "strong monotonicity" and proves that a prefix code is optimal for a given source if and only if it is complete and strongly monotone.
Key highlights:
- Huffman codes are known to be optimal, but not all optimal codes are Huffman codes.
- The sibling property characterizes Huffman codes, but no analogous characterization was known for the broader class of optimal prefix codes.
- The authors introduce the concept of "strong monotonicity" which generalizes the monotonicity property.
- They prove that a prefix code is optimal if and only if it is complete and strongly monotone.
- This provides a necessary and sufficient characterization of optimal prefix codes, which was an open question until now.
- The result is exploited in another recent work to prove results about the competitive optimality of Huffman codes.
Cytaty
"A property of prefix codes called strong monotonicity is introduced, and it is proven that for a given source, a prefix code is optimal if and only if it is complete and strongly monotone."
"Theorem 1.1. A prefix code is optimal if and only if it is complete and strongly monotone."