compression.slides.printing

The combinations form a binary tree structure that

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from Step 2 until there’s just one symbol left. The “combinations” form a binary tree structure that can be encoded using a single bit for each level.
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Compression Entropy Coding Huffman Coding Message Probability Information Both Heads 1/4 2 bits Both Tails 1/4 2 bits One Each 1/2 1 bits 2H 2T H+T 0 1 1 0 Properties: Decoding is just traversing the tree: When you reach a leaf, emit symbol and start a new one Prefix property (required for variable-length codes): No symbol’s code appears as the beginning of a longer one Each symbol is encoded with approximately - log 2 p ( a ) bits.
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Compression Entropy Coding Arithmetic Coding Huffman encodes symbols one-by-one, so you have to “round up” the bit allocation Arithmetic coding doesn’t use a one-to-one mapping between symbols and bit patterns The entire string is encoded as one (long) real number
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Compression Entropy Coding Vector Quantization Divide the signal into sets of n values and treat each as one collective vector value. Quantize the vectors to some finite number of them—this causes loss but reduces the space of possible values. Use a unique code for each vector and transmit that code instead. Most VQ systems intelligently select the quantization based on the signal content—this means you have to send the codebook. Can extend to images using n × m blocks. Example: 4 x 4 blocks, 256 levels/pixel = 256 16 possibilities = 128 bits/block Choose 4096 possibilities = 12 bits/block
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