Information Theory: Data Compression & Huffman Code

What is the primary goal of data compression?

What must the expected description length of a coding scheme be compared to the entropy?

What characteristic of Huffman Codes ensures they can be decoded without ambiguity?

How are the nodes combined when constructing a Huffman tree?

In Huffman coding, what does the codeword for each symbol consist of?

How should the probabilities of symbols be arranged when designing a Huffman code?

What does the term 'instantaneous code' refer to in the context of Huffman coding?

Which of the following statements is true regarding Huffman codes?

Data Compression

Data compression reduces the size of data by assigning shorter codes to frequent outcomes.
The goal is to achieve the shortest average description length of a random variable.
An instantaneous code allows for decoding without ambiguity, ensuring that no code is a prefix of another.

Key Concepts

The expected description length must meet or exceed the entropy of the data source.
Entropy serves as a measure of the efficiency of code lengths in information theory.

Huffman Coding

Huffman coding is a systematic method for creating optimal variable-length codes based on symbol probabilities.
The resulting codes are both uniquely decodable and instantaneous.

Huffman Coding Algorithm

Treat probabilities (Pi) as leaf nodes of a binary tree, sorting them in descending order.
Construct the Huffman tree by:
- Iteratively merging the two nodes with the lowest probabilities to create a new node.
- Assign a binary digit (0 or 1) to each branch during the merging process.
The codeword for each symbol derives from the sequence of binary digits from the root of the tree to its corresponding leaf node.

Example

Consider symbols s1, s2, s3, and s4 with probabilities ½, ¼, 1/8, and 1/8, respectively, showcasing Huffman coding in action.

Explore the concepts of data compression and Huffman coding in this quiz. Learn how to assign short descriptions to frequent outcomes and calculate the shortest average description length. Test your understanding of entropy and its role in efficient coding.