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Huffman Coding with Non-Sorted Frequencies Shmuel Tomi Klein Dana Shapira Bar Ilan University, Ashkelon Academic College, ISRAEL
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Outline Background and motivation Using non-sorted frequencies Relevance to other compression Conclusions Dynamic compression of data packets Background and motivation Using non-sorted frequencies Dynamic compression of data packets Relevance to other compression Conclusions
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Sorted frequencies Sufficient but not necessary Huffman’s algorithm Construction in Code construction only
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Applications Low text / code ratio Several codes Markov process encoding Dynamic coding schemes: Encoding based on
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Optimal Trees 2 54 3 32 13 9 76 22 Huffman Tree 7 5 3 3 2 2 7 5 4 3 3 7 6 5 4 9 7 6 13 9 22
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2 55 3 23 1210 75 22 Optimal Trees 7 5 3 2 3 2 7 5 5 3 2 7 5 5 5 10 7 5 12 10 22 Non-Huffman Tree
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2 64 3 32 1210 75 22 Optimal Trees 7 5 3 3 2 2 7 5 4 3 3 7 5 6 4 10 7 5 12 10 22 Non-Huffman Tree
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No restriction bad encoding 1 1 2 4 8 16 32 2n2n 1 1 2 4 8 16 2n2n
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Restriction: order operations 7 5 3 3 2 2 2213 9 7 9 6 7 5 6 4 7 5 3 3 4
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Start with any order Then use 2 queues Reversed order full tree
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Partial Sort: parameter K W1W1 WKWK...W3W3 W2W2 Time: 4-grams3-grams2-grams1-gramsTests:21886602680852English 56078188642965131French
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Average # bits/char vs # partition blocks English 2832128512 3 4 5 6 7 2048 1-grams 2-grams 3-grams 4-grams
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French Average # bits/char vs # partition blocks 2832128512 3 4 5 6 7 2048 1-grams 2-grams 3-grams 4-grams
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Dynamic compression of data packets Encoding based on
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Bub- For-5 BubbleBlocked Block size Bigrams 5.065.063.812000 Comprs 5.065.063.8120000 11.67.330.12000 Time 15.211.137.420000 6.356.344.112000 Comprs 6.346.344.1120000 14.09.9286.22000 Time 17.613.4290.420000 French English
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Relevance to other compression schemes Arithmetic coding 256-ary Huffman (s,c)-dense codes, Fibonacci codes Burrows-Wheeler Transform
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Conclusion Not fully sorting the weights Time savings for sort intensive methods Compresion / Time tradeoff
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