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Arithmetic Coding Ppt Full Description SaveArithmetic Coding Uploaded by Rakesh Inani 0 ratings 0 found this document useful (0 votes) 21 views 18 pages Document Information click to expand document information Description: arithmatic Date uploaded Nov 21, 2014 Copyright All Rights Reserved Available Formats PPTX, PDF, TXT or read online from Scribd Share this document Share or Embed Document Sharing Options Share on Facebook, opens a new window Facebook Share on Twitter, opens a new window Twitter Share on LinkedIn, opens a new window LinkedIn Share with Email, opens mail client Email Copy Text Copy Link Did you find this document useful 0 0 found this document useful, Mark this document as useful 0 0 found this document not useful, Mark this document as not useful Is this content inappropriate Report this Document Download Now Save Save Arithmetic Coding For Later 0 ratings 0 found this document useful (0 votes) 21 views 18 pages Arithmetic Coding Uploaded by Rakesh Inani Description: arithmatic Full description Save Save Arithmetic Coding For Later 0 0 found this document useful, Mark this document as useful 0 0 found this document not useful, Mark this document as not useful Embed Share Print Download Now Jump to Page You are on page 1 of 18 Search inside document.
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Copy and paste following PHP program in test.php file and keep it in your PHP Servers document root and browse it using any browser. ![]() Arithmetic Coding Uploaded by RohitSharma 0 ratings 0 found this document useful (0 votes) 18 views 30 pages Document Information click to expand document information Description: Arithmetic Coding Date uploaded Sep 14, 2014 Copyright All Rights Reserved Available Formats PPT, PDF, TXT or read online from Scribd Share this document Share or Embed Document Sharing Options Share on Facebook, opens a new window Facebook Share on Twitter, opens a new window Twitter Share on LinkedIn, opens a new window LinkedIn Share with Email, opens mail client Email Copy Text Copy Link Did you find this document useful 0 0 found this document useful, Mark this document as useful 0 0 found this document not useful, Mark this document as not useful Is this content inappropriate Report this Document Download Now Save Save Arithmetic Coding For Later 0 ratings 0 found this document useful (0 votes) 18 views 30 pages Arithmetic Coding Uploaded by RohitSharma Description: Arithmetic Coding Full description Save Save Arithmetic Coding For Later 0 0 found this document useful, Mark this document as useful 0 0 found this document not useful, Mark this document as not useful Embed Share Print Download Now Jump to Page You are on page 1 of 30 Search inside document. If you continue browsing the site, you agree to the use of cookies on this website. If you wish to opt out, please close your SlideShare account. Among all the other tasks they get assigned in college, writing essays is one of the most difficult assignments. Fortunately for students, there are many offers nowadays which help to make this process easier. Fortunately, it is possible to rescale the intervals and use only integer arithmetic for a practical implementation. Normally, a string of characters such as the words hello there is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not - so - frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding such as Huffman coding in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, a fraction n where (0.0 n ALGORITHM ARITHMETIC CODING ENCODER Arithmetic coding: encode symbols CAEE: (a) probability distribution of symbols; (b) graphical display of shrinking ranges; (c) new low, high, and range generated The encoding process is illustrated in the above figures (h) and (c), in which a string of symbols CAEE is encoded. After the second symbol A, low, high, and range are 0.30, 0.34, and 0.04. The process repeats itself until after the terminating symbol is received. By then low and high are 0.33184 and 0.33220, respectively. Arithmetic Coding Ppt Pc X PAIt is apparent that finally we have range - Pc x PA x PE x PE x Ps 0.2 x 0.2 x 0.3 X 0.3 x 0.1 0.00036 The final step in encoding calls for generation of a number that falls within the range low, high). Arithmetic Coding Ppt How To Do ItAlthough it is trivial to pick such a number in decimal, such as 0.33184, 0.33185, or 0.332 in the above example, it is less obvious how to do it with a binary fractional number. The following algorithm will ensure that the shortest binary codeword is found if low and high are the two ends of the range and low PROCEDURE Generating Codeword for Encoder For the above example, low 0.33184, high 0.3322. If we assign 1 to the first binary fraction bit, it would be 0.1 in binary, and its decimal value(code) value(0.l) 0.5 high. Hence, we assign 0 to the first bit. Assigning 1 to the second bit makes a binary code 0.01 and value (0.01) 0.25, which is less than high, so it is accepted. Since it is still true that value(0.0l) the iteration continues. Eventually, the binary codeword generated is 0.01010101, which is 2 - 2 2 - 4 2 - 6 2 - 8 0.33203125. It must be pointed out that we were lucky to have found a codeword of only 8 bits to represent this sequence of symbols CAEE. ![]() Namely, in the worst case, the shortest codeword in arithmetic coding will require k bits to encode a sequence of symbols, and where Pi is the probability for symbol i and range is the final range generated by the encoder. Apparently, when the length of the message is long, its range quickly becomes very small, and hence log2 1 range becomes very large; the difference between log2 1 rangeand log21 range is negligible. Generally, Arithmetic Coding achieves better performance than Huffman coding, because the former treats an entire sequence of symbols as one unit, whereas the latter has the restriction of assigning an integral number of bits to each symbol. For example, Huffman coding would require 12 bits for CAEE, equaling the worst - case performance of Arithmetic Coding. Moreover, Huffman coding cannot always attain the upper bound illustrated in Eq. It can be shown (see Exercise ) that if the alphabet is A, B, C and the known probability distribution is Pa 0.5, PB 0.4, Pc 0.1, then for sending BBB, Huffman coding will require 6 bits, which is more than, whereas arithmetic coding will need only 4 bits. ALGORITHM ARITHMETIC CODING DECODER The following table illustrates the decoding process for the above example. Initially, value 0.33203125. Since Range low(C) 0.3 Range high(C), the first output symbol is C. This yields value - 0.33203125 - 0.3J 0.2 0.16015625, which in turn determines that the second symbol is A. Eventually, value is 0.953125, which falls in the range of the terminator. Table Arithmetic coding: decode symbols CAEE The algorithm described previously has a subtle implementation difficulty. When the intervals shrink, we need to use very high - precision numbers to do encoding. This makes practical implementation of this algorithm infeasible.
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