By Stefan M. Moser

ISBN-10: 1107015839

ISBN-13: 9781107015838

ISBN-10: 1107601967

ISBN-13: 9781107601963

This easy-to-read consultant presents a concise advent to the engineering historical past of contemporary communique platforms, from cell phones to information compression and garage. heritage arithmetic and particular engineering innovations are stored to a minimal in order that just a uncomplicated wisdom of high-school arithmetic is required to appreciate the fabric lined. The authors commence with many sensible purposes in coding, together with the repetition code, the Hamming code and the Huffman code. They then clarify the corresponding details thought, from entropy and mutual info to channel potential and the data transmission theorem. ultimately, they supply insights into the connections among coding idea and different fields. Many labored examples are given through the e-book, utilizing sensible purposes to demonstrate theoretical definitions. workouts also are incorporated, permitting readers to double-check what they've got realized and achieve glimpses into extra complex subject matters, making this excellent for someone who wishes a short advent to the topic

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Example text

49) 3 the occurrence of an error is detected. For instance, consider the case of a single error in the ith position such that yi = xi + 1 and y = x , ∀ ∈ {1, 2, . . , 6} \ {i}. 51) if i = 5, if i = 6. Therefore, all single errors can be successfully detected. In addition, consider the case of a double error in the ith and jth positions, respectively, such that yi = xi + 1, y j = x j + 1, and y =x , ∀ ∈ {1, 2, . . , 6} \ {i, j}. 53) if (i, j) = (2, 6), y5 = y1 + y3 , y6 = y2 + y3 if (i, j) = (3, 4), if (i, j) = (3, 5), if (i, j) = (3, 6), y5 = y1 + y3 if (i, j) = (4, 5), y6 = y2 + y3 if (i, j) = (4, 6), y6 = y2 + y3 if (i, j) = (5, 6).

2. 3 Special type of parity check to protect against burst errors of maximum length L = 8 H = (110)8 = e = (145)8 = l = (154)8 = l = (154)8 = o = (157)8 = SP= (040)8 = N = (116)8 = C = (103)8 = T = (124)8 = U = (125)8 = Check sum = 01001000 01100101 01101100 01101100 01101111 00100000 01001110 01000011 01010100 01010101 01101110 = n where n is the parity-check symbol. 4, is met during the transmission of the above message, where the bold-face positions are in error. In this case, the burst error is successfully detected since the check sum is not 00000000.

Therefore, all single errors can be successfully detected. In addition, consider the case of a double error in the ith and jth positions, respectively, such that yi = xi + 1, y j = x j + 1, and y =x , ∀ ∈ {1, 2, . . , 6} \ {i, j}. 53) if (i, j) = (2, 6), y5 = y1 + y3 , y6 = y2 + y3 if (i, j) = (3, 4), if (i, j) = (3, 5), if (i, j) = (3, 6), y5 = y1 + y3 if (i, j) = (4, 5), y6 = y2 + y3 if (i, j) = (4, 6), y6 = y2 + y3 if (i, j) = (5, 6). Hence, this code can detect any pattern of double errors.

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


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