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By Feng Wu

Visible details is without doubt one of the richest and so much bandwidth-consuming modes of conversation. to fulfill the necessities of rising functions, strong facts compression and transmission options are required to accomplish hugely effective verbal exchange, even within the presence of growing to be conversation channels that provide elevated bandwidth.Presenting the result of the author's years of analysis on visible data Read more...

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We have a source S that generates symbols from the alphabet A . It is from a finite alphabet and satisfies the AEP. The sequence of symbols Sn = {S1 , S2 , · · · , Sn } is sent over the channel so that the receiver can reconstruct the sequence. Assume the one stage coding is considered. We map the sequence onto a codeword Y n (Sn ) and send the codeword over the channel. The receiver looks at his received sequence Yˆ n and makes an estimation Sˆn of the sequence Sn that was sent. The receiver makes an error if (n) Sˆn = Sn .

4) Hamming code produces 7 bits of output for every 4 bits of input. 58)  0 0 1 1 0 1 0 . 0001101 The codewords are obtained as a linear combination of the rows of G, where all the operations are computed as modulo 2 in each vector element. That is, the code is the row space of G. For a source vector x = [x1 , x2 , x3 , x4 ], the codeword is y = xG. 59) ✐ ✐ ✐ ✐ ✐ ✐ ✐ ✐ 18 1 Information Theory For example, if x = [0, 0, 1, 1], the codeword is y = [0, 0, 1, 1, 0, 1, 0] + [0, 0, 0, 1, 1, 0, 1] = [0, 0, 1, 0, 1, 1, 1].

First, we introduce the concept of entropy, which is the minimum length for lossless compression of a source, according to Shannon’s source coding theorem. Huffman coding and arithmetic coding are taken as examples to explain what source coding is and how a source is compressed toward its entropy. The rate distortion theorem is also discussed because of its importance to guiding the lossy compression of a source. Second, we introduce the concept of channel capacity, which is the maximum rate that a channel can be used with negligible transmission errors, according to Shannon’s channel coding theorem.

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