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

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

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

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

Optimal Trees Huffman Tree

Optimal Trees Non-Huffman Tree

Optimal Trees Non-Huffman Tree

No restriction bad encoding n2n n2n

Restriction: order operations

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

Partial Sort: parameter K W1W1 WKWK...W3W3 W2W2 Time: 4-grams3-grams2-grams1-gramsTests: English French

Average # bits/char vs # partition blocks English grams 2-grams 3-grams 4-grams

French Average # bits/char vs # partition blocks grams 2-grams 3-grams 4-grams

Dynamic compression of data packets Encoding based on

Bub- For-5 BubbleBlocked Block size Bigrams Comprs Time Comprs Time French English

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

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