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GSU CSC 2320 - Huffman Encoding

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Huffman EncodingText Compression (Zip)ASCII CodesFirst ApproachOf Course!!However…Prefix CodesFor ExampleHow do we find the optimal coding tree?Constructing a Huffman CodeSlide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Decode the treeIn class practiceHuffman EncodingDr. Bernard Chen Ph.D.University of Central ArkansasText Compression (Zip)On a computer: changing the representation of a file so that it takes less space to store or/and less time to transmit.Original file can be reconstructed exactly from the compressed representationASCII CodesLet the wordFirst ApproachLet the wordHow to write this string in a most economical way?Since it has 5 words, 3 bit to represent it is required!!Is there a better way?Of Course!!However…There are some concerns…Suppose we have A-> 01B-> 0101If we have 010101, is this AB? BA? Or AAA?Therefore: prefix codes, no codeword is a prefix of another codeword, is necessaryPrefix CodesAny prefix code can be represented by a full binary treeEach leaf stores a symbol.Each node has two children – left branch means 0, right means 1.codeword = path from the root to the leaf interpreting suitably the left and right branchesFor ExampleA = 0B = 100C = 1010D = 1011R = 11Decoding is unique and simple!How do we find the optimal coding tree?it is clear that the two symbols with the smallest frequencies must be at the bottom of the optimal tree, as children of the lowest internal nodeThis is a good sign that we have to use a bottom-up manner to build the optimal code!Huffman’s idea is based on a greedy approach, using the previous notices.Constructing a Huffman CodeAssume that frequencies of symbols are A: 50 B: 15 C: 10 D: 10 R: 18Smallest numbers are 10 and 10 (C and D)Constructing a Huffman CodeNow Assume that frequencies of symbols are A: 50 B: 15 C+D: 20 R: 18C and D have already been used, and the new node above them (call it C+D) has value 20The smallest values are B + RConstructing a Huffman CodeNow Assume that frequencies of symbols are A: 50 B+R: 33 C+D: 20The smallest values are (B + R)+(C+D)=53Constructing a Huffman CodeNow Assume that frequencies of symbols are A: 50 (B+R) + (C+D): 53The smallest values are A+ ((B + R)+(C+D))=103Constructing a Huffman CodeConstructing a Huffman CodeAssume that frequencies of symbols are A: 50 B: 20 C: 10 D: 10 R: 30Smallest numbers are 10 and 10 (C and D)Constructing a Huffman CodeAssume that frequencies of symbols are A: 50 B: 20 C: 10 D: 10 R: 30C and D have already beenused, and the new node above them (call it C+D) has value 20The smallest values are B, C+DConstructing a Huffman CodeAssume that frequencies of symbols are A: 50 B: 20 C: 10 D: 10 R: 30Next, B+C+D (40) and R (30)Constructing a Huffman CodeAssume that frequencies of symbols are A: 50 B: 20 C: 10 D: 10 R: 30Finally:Constructing a Huffman CodeDecode the treeSuppose we have the Following code:10001011What is the decode result?In class practiceA: 10B: 10C: 25D: 15E: 30F: 21What is the Huffman Encoding


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GSU CSC 2320 - Huffman Encoding

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