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This summary is machine-generated.

This study introduces m-gram entropy variable-to-variable coding, extending Huffman coding for symbol sequences. An approximate linear-complexity approach yields results close to optimal and surpasses DEFLATE/PPM for certain data.

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Area of Science:

  • Information Theory
  • Computer Science
  • Data Compression

Background:

  • Classical Huffman coding is limited to single symbols.
  • Variable-to-variable coding for symbol sequences (m-grams) is an extension.

Purpose of the Study:

  • To extend Huffman coding for m-gram entropy variable-to-variable coding.
  • To develop an optimal algorithm and an efficient approximate approach for m-gram coding.

Main Methods:

  • Developed a procedure for determining m-gram frequencies.
  • Formulated an optimal coding algorithm with O(mn2) complexity.
  • Proposed a greedy heuristic-based approximate approach with linear complexity.

Main Results:

  • The optimal algorithm's complexity is O(mn2).
  • The approximate approach achieves near-optimal results.
  • The approximate approach outperforms DEFLATE and PPM on data with stable statistics.

Conclusions:

  • The proposed approximate method offers a practical solution for m-gram entropy coding.
  • This approach is particularly effective for data with predictable statistical properties.