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By Chandramouli Memon Rabbani
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Example text
8N-2, HN-l. 3. We repeat the previous step until the final set has only one member. The recursive procedure in Step 2 can be viewed as the construction of a binary tree, since at each step we are merging two symbols. At the end of the recursion process, all the symbols 81,82, .. , 8 N will be leaf nodes of this tree. The codeword for each symbol 8i is obtained by traversing the binary tree from its root to the leaf node corresponding to 8i. 3. The input data to be compressed is composed of symbols in the alphabet k, l, U, w, e, r, ?
At each entry we form the two-tuple (Si, Li). Decoding using the lookup table approach is relatively easy: 24 CHAPTER 2 1. From the compressed input bit stream, we read in L bits into a buffer. 2. We use the L-bit word in the buffer as an address into the lookup table and obtain the corresponding symbol, say Sk. Let the codeword length be lk. We have now decoded one symbol. 3. We discard the first lk bits from the buffer and we append to the buffer, the next lk bits from the input, so that the buffer has again L bits.
For instance, in the Huffman tables for the JPEG image compression standard, there should be no Huffman codeword that is all ones; that is, 11111 ... 1. If the codeword design method yields such a sequence, one can simply take the complement of such a code table. The complement of a Huffman code table is also a valid Huffman code table and will satisfy the unique prefix condition that is characteristic of all Huffman codewords. 8 ARITHMETIC CODING The Huffman coder generates a new codeword for each input symbol.