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Better Algorithms for Constructing Minimum Cost Markov Chains and AIFV Codes
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Better Algorithms for Constructing Minimum Cost Markov Chains and AIFV Codes

Golin, M. J

Better Algorithms for Constructing Minimum Cost Markov Chains and AIFV Codes

Golin, M. J ; Sharif University of Technology | 2024

185 Viewed
  1. Type of Document: Article
  2. DOI: 10.1109/ISIT57864.2024.10619633
  3. Publisher: 2024
  4. Abstract:
  5. Almost Instantaneous Fixed to Variable (AIFV) coding is a relatively new method of loss less coding that, unlike Huffman coding, uses more than one coding tree. The problem of constructing optimal AIFV codes is a special case of that of constructing minimum cost Markov Chains. This paper provides the first complete proof of correctness for the previously known iterative algorithm for constructing such Markov chains. A recent work describes how to efficiently solve the Markov Chain problem by first constructing a Markov Chain Polytope and then running the Ellipsoid algorithm for linear programming on it. This paper's second result is that, in the AIFV case, a special property of the polytope instead permits solving the corresponding linear program using simple binary search. © 2024 IEEE
  6. Keywords:
  7. Integer linear programming ; Problem solving ; Trees (mathematics) ; Turbo codes ; Ellipsoid algorithm ; Huffman coding ; Iterative algorithm ; Linear programs ; Linear-programming ; Minimum cost ; Polytopes ; Proof of correctness ; Simple++ ; Special properties ; Markov chains
  8. Source: IEEE International Symposium on Information Theory - Proceedings ; 2024 , Pages 61-66 ; 21578095 (ISSN); 979-835038284-6 (ISBN)
  9. URL: https://ieeexplore.ieee.org/document/10619633?signout=success