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Shannon coding
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<h2 id="example">Example</h2> <p>In the table below is an example of creating a code scheme for symbols <i>a</i>1 to <i>a</i>6. The value of <i>l</i><i>i</i> gives the number of bits used to represent the symbol <i>a</i><i>i</i>. The last column is the bit code of each symbol. </p> <table><tbody><tr><th><i>i</i></th><th><i>p</i><i>i</i></th><th><i>l</i><i>i</i></th><th> ∑ n = 0 i − 1 p n {\displaystyle \sum _{n=0}^{i-1}p_{n}} </th><th>Previous value in binary</th><th>Codeword for <i>a</i><i>i</i></th></tr><tr><th>1</th><td>0.36</td><td>2</td><td>0.0</td><td>0.0000</td><td>00</td></tr><tr><th>2</th><td>0.18</td><td>3</td><td>0.36</td><td>0.0101...</td><td>010</td></tr><tr><th>3</th><td>0.18</td><td>3</td><td>0.54</td><td>0.1000...</td><td>100</td></tr><tr><th>4</th><td>0.12</td><td>4</td><td>0.72</td><td>0.1011...</td><td>1011</td></tr><tr><th>5</th><td>0.09</td><td>4</td><td>0.84</td><td>0.1101...</td><td>1101</td></tr><tr><th>6</th><td>0.07</td><td>4</td><td>0.93</td><td>0.1110...</td><td>1110</td></tr></tbody></table> <p>Shannon, Claude Elwood. <a href="https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf">"A Mathematical Theory of Communication."</a> ACM SIGMOBILE mobile computing and communications review 5.1 (2001): 3-55. </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Shannon, Claude E. (July 1948). "A Mathematical Theory of Communication [reprint with corrections]" (PDF). Bell System Technical Journal. 27 (3): 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x. hdl:11858/00-001M-0000-002C-4314-2. <a href="/wiki/Claude_Shannon" target="_blank">/wiki/Claude_Shannon</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Ze-Nian Li; Mark S. Drew; Jiangchuan Liu (9 April 2014). Fundamentals of Multimedia. Springer Science & Business Media. ISBN 978-3-319-05290-8. <a href="978-3-319-05290-8" target="_blank">978-3-319-05290-8</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>