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Huffman Coding with Non-Sorted Frequencies

Huffman Coding with Non-Sorted Frequencies. Shmuel Tomi Klein Dana Shapira Bar Ilan University, Ashkelon Academic College, ISRAEL. Background and motivation. Using non-sorted frequencies. Dynamic compression of data packets. Relevance to other compression. Conclusions. Outline.

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Huffman Coding with Non-Sorted Frequencies

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  1. Huffman Coding with Non-Sorted Frequencies Shmuel Tomi Klein Dana Shapira Bar Ilan University, Ashkelon Academic College, ISRAEL

  2. Background and motivation Using non-sorted frequencies Dynamic compression of data packets Relevance to other compression Conclusions Outline Background and motivation Using non-sorted frequencies Dynamic compression of data packets Relevance to other compression Conclusions

  3. Huffman’s algorithm Construction in Sorted frequencies Sufficient but not necessary Code construction only

  4. Low text / code ratio Several codes Markov process encoding Dynamic coding schemes: Encoding based on Applications

  5. 7 5 3 3 2 2 22 7 5 4 3 3 13 9 7 6 5 4 7 6 5 4 9 7 6 13 9 3 3 2 2 22 Huffman Tree Optimal Trees

  6. Optimal Trees 7 5 3 2 3 2 22 7 5 5 3 2 12 10 7 5 5 5 7 5 5 5 10 7 5 12 10 3 2 3 2 22 Non-Huffman Tree

  7. Optimal Trees 7 5 3 3 2 2 22 7 5 4 3 3 12 10 7 5 6 4 7 5 6 4 10 7 5 12 10 3 3 2 2 22 Non-Huffman Tree

  8. No restriction bad encoding 2n 1 32 1 16 2 8 4 4 8 2 16 1 1 2n

  9. Restriction: order operations 7 5 3 3 2 2 7 9 6 7 5 3 3 4 13 9 7 5 6 4 22

  10. Reversed order full tree Start with any order Then use 2 queues

  11. W1 W2 W3 . . . WK Time: Partial Sort: parameter K

  12. English 2-grams 7 3-grams 6 4-grams 5 4 3 2 8 32 128 512 2048 Average # bits/char vs # partition blocks 1-grams

  13. 1-grams 2-grams 3-grams 4-grams Average # bits/char vs # partition blocks French 7 6 5 4 3 2 8 32 128 512 2048

  14. Encoding based on Dynamic compression of data packets

  15. English French

  16. Arithmetic coding 256-ary Huffman (s,c)-dense codes, Fibonacci codes Burrows-Wheeler Transform Relevance to other compression schemes

  17. Not fully sorting the weights Time savings for sort intensive methods Conclusion Compresion / Time tradeoff

  18. Thank you !

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