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Write procedure to decode Arithmetic Coding Tag.

Decoding Arithmetic Codes: A Step-by-Step Guide

Understanding the Input

  • Encoded data: The arithmetic code tag (a single floating-point number).
  • Probability model: The probability distribution of symbols used during encoding. This is crucial for decoding. Must be identical to the encoder's model.
  • Symbol alphabet: The set of all possible symbols.

Decoding Algorithm

  • Initialize lower bound (L) to 0.0 and upper bound (U) to 1.0.
  • Obtain the encoded value.
  • Iterate through the following steps until a symbol is decoded:
    • Calculate the range size (U - L). 
    • For each symbol in the alphabet: 
    • Calculate the cumulative probability (C) up to that symbol. 
    • If the encoded value falls within the interval [L + C * range size, L + (C + P) * range size), where P is the symbol probability, then decode the symbol. 
    • Update the lower and upper bounds: * L = L + C * range size * U = L + (C + P) * range size
  • Repeat step 3 until the entire encoded sequence is decoded.
  • Handle potential precision errors gracefully; adjustments might be needed in the final decoding steps.

Output

  • Decoded symbol sequence: The original data reconstructed from the code.

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