✨The huffman extension and contraction are inverses of each other.
🔑The extension lemma states that an optimal code for p' is also optimal for p if it's the huffman extension.
📊The expected codeword lengths of p' and its extension can be related using the lengths of the original code.
🗂️The contraction of a sibling code results in a code with non-decreasing lengths.
🔍The expected codeword length can be used to compare the optimality of different codes.
What is the huffman extension?
—The huffman extension is the process of adding a binary digit to the last code word in an optimal prefix code.
What is the huffman contraction?
—The huffman contraction is the process of merging two sibling code words in an optimal prefix code.
What does the extension lemma state?
—The extension lemma states that if an optimal code is created for a pmf p', its huffman extension is also optimal for a pmf p.
How are the expected codeword lengths related?
—The expected codeword length of a contracted code can be related to the expected codeword length of its sibling code and the probabilities of the merged symbols.
Why is the sibling code lemma important?
—The sibling code lemma provides a way to create a contraction of a code, which is necessary to define the huffman contraction.
00:00Introduction to the huffman extension and contraction.
01:10Explanation of the extension lemma and its significance.
03:42Relating the expected codeword lengths of the contracted and original codes.
05:22Overview of the sibling code and huffman contraction.
07:14Showing the relationship between the lengths of contracted and original code words.
