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A Student’s Guide to Coding and Information Theory - download pdf or read online

By Stefan M. Moser

ISBN-10: 1107015839

ISBN-13: 9781107015838

ISBN-10: 1107601967

ISBN-13: 9781107601963

This easy-to-read consultant presents a concise creation to the engineering heritage of contemporary communique structures, from cellphones to facts compression and garage. heritage arithmetic and particular engineering recommendations are saved to a minimal in order that just a easy wisdom of high-school arithmetic is required to appreciate the cloth lined. The authors start with many useful functions in coding, together with the repetition code, the Hamming code and the Huffman code. They then clarify the corresponding info concept, from entropy and mutual details to channel means and the data transmission theorem. ultimately, they supply insights into the connections among coding thought and different fields. Many labored examples are given through the publication, utilizing useful purposes to demonstrate theoretical definitions. workouts also are integrated, allowing readers to double-check what they've got realized and achieve glimpses into extra complex themes, making this excellent for someone who wishes a brief advent to the topic

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Extra info for A Student’s Guide to Coding and Information Theory

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3. 3 Venn diagram used for decoding (1 1 1 0 1 0 0). as before, we see that the error must lie in circle I, but cannot be in circles II and III. Hence the only possible erroneous bit is p1 . Changing the read-out of p1 from 1 to 0 will correct the one-bit error. Now let us revisit the above two error-correcting examples and try to formulate a more systematic approach. In the first example, the read-out was y = (0 1 1 1 1 0 0). 3 Hamming code the following connection:  1  HyT =  0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1   0   1       1 1 1         0 1 = 1      0 1 1   0   0 ⇐⇒   I    II  .

4(a). 4(b) (you might want to think of them as highdimensional balls), each with radius R = 1, centered at x and x , respectively, these two spheres would not overlap and must be well-separated. Points within the x-sphere represent the read-outs that are at a distance of at most 1 from x. In other words, the points within the x-sphere are either x or x with a one-bit error. 4 Geometry of x = x in the (7, 4) Hamming code with Hamming distance 3. If we draw a sphere with radius R = 1 centered at each codeword of the (7, 4) Hamming code, there will be 16 nonoverlapping spheres since there are 16 codewords and every pair of distinct codewords is separated by a distance of at least 3.

4(a). 4(b) (you might want to think of them as highdimensional balls), each with radius R = 1, centered at x and x , respectively, these two spheres would not overlap and must be well-separated. Points within the x-sphere represent the read-outs that are at a distance of at most 1 from x. In other words, the points within the x-sphere are either x or x with a one-bit error. 4 Geometry of x = x in the (7, 4) Hamming code with Hamming distance 3. If we draw a sphere with radius R = 1 centered at each codeword of the (7, 4) Hamming code, there will be 16 nonoverlapping spheres since there are 16 codewords and every pair of distinct codewords is separated by a distance of at least 3.

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A Student’s Guide to Coding and Information Theory by Stefan M. Moser


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