Shannon coding

In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding does, and never better than but sometimes equal to the Shannon–Fano coding (Fano's method). The method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article "A Mathematical Theory of Communication", and is therefore a centerpiece of the information age. Shannon–Fano coding methods gave rise to the field of information theory and without its contributions, the world would not have any of the many successors; for example Huffman coding, or arithmetic coding. Much of our day-to-day lives are significantly influenced by digital data and this would not be possible without Shannon-Fano coding and the ongoing evolution of its methods. In Shannon coding, the symbols are arranged in order from most probable to least probable, and assigned codewords by taking the first l_i = \left\lceil -\log_2 p_i \right\rceil bits from the binary expansions of the cumulative probabilities \sum\limits_{k=0}^{i-1} p_k.…

In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding does, and never better than but sometimes equal to the Shannon–Fano coding (Fano's method). The method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article "A Mathematical Theory of Communication", and is therefore a centerpiece of the information age. Shannon–Fano coding methods gave rise to the field of information theory and without its contributions, the world would not have any of the many successors; for example Huffman coding, or arithmetic coding. Much of our day-to-day lives are significantly influenced by digital data and this would not be possible without Shannon-Fano coding and the ongoing evolution of its methods. In Shannon coding, the symbols are arranged in order from most probable to least probable, and assigned codewords by taking the first l_i = \left\lceil -\log_2 p_i \right\rceil bits from the binary expansions of the cumulative probabilities \sum\limits_{k=0}^{i-1} p_k. Here \lceil x \rceil denotes the ceiling function (which rounds x up to the next integer value). ==References== Shannon, Claude Elwood. "A Mathematical Theory of Communication." ACM SIGMOBILE mobile computing and communications review 5.1 (2001): 3-55.

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