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Questions and Answers
What is the primary goal of data compression?
What is the primary goal of data compression?
- To eliminate all data redundancy
- To assign short descriptions to the most frequent outcomes (correct)
- To assign longer descriptions to infrequent outcomes
- To ensure data is stored without any loss of quality
What must the expected description length of a coding scheme be compared to the entropy?
What must the expected description length of a coding scheme be compared to the entropy?
- Both greater and equal to the entropy
- Less than the entropy
- Equal to the entropy
- Greater than the entropy (correct)
What characteristic of Huffman Codes ensures they can be decoded without ambiguity?
What characteristic of Huffman Codes ensures they can be decoded without ambiguity?
- They use numeric values in their coding
- They are uniquely decodable and instantaneous (correct)
- They are all the same length
- They can be assigned multiple meanings
How are the nodes combined when constructing a Huffman tree?
How are the nodes combined when constructing a Huffman tree?
In Huffman coding, what does the codeword for each symbol consist of?
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?
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?
What does the term 'instantaneous code' refer to in the context of Huffman coding?
Which of the following statements is true regarding Huffman codes?
Which of the following statements is true regarding Huffman codes?
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Study Notes
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.
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