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Explain Modeling and Coding with suitable example.

Data Compression: Mastering Modeling and Coding Techniques

What is Modeling in Data Compression?

  • A model statistically represents the data's characteristics.
  • Predicts the probability of each symbol or sequence appearing.
  • Reduces redundancy by focusing on frequent patterns.
  • Examples: Huffman coding uses frequency models; arithmetic coding uses probabilistic models.

Types of Models in Data Compression

  • Statistical Models: Assign probabilities to symbols based on their frequency.
  • Predictive Models: Predict the next symbol based on preceding symbols (e.g., LZ77).
  • Context Modeling: Considers the context surrounding a symbol to improve prediction.

What is Coding in Data Compression?

  • Translates the model's output into a compressed bitstream.
  • Assigns shorter codes to more frequent symbols (or sequences).
  • Achieves compression by representing data using fewer bits.
  • Examples: Huffman coding assigns variable-length codes; run-length encoding uses fixed-length codes for repeated symbols.

Example: Huffman Coding

  • Modeling: Analyze the input text "aaabbc" to determine symbol frequencies (a:3, b:2, c:1).
  • Coding: Construct a Huffman tree based on frequencies. 'a' gets the shortest code, 'c' the longest.
  • Assign codes: a = 0, b = 10, c = 11.
  • Encode "aaabbc": 000101011.
  • Decoding reverses the process using the Huffman tree.

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