Read e-book online A Student’s Guide to Coding and Information Theory PDF

By Stefan M. Moser

ISBN-10: 1107015839

ISBN-13: 9781107015838

ISBN-10: 1107601967

ISBN-13: 9781107601963

This easy-to-read advisor offers a concise creation to the engineering historical past of contemporary communique platforms, from cell phones to facts 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 cloth coated. 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 info idea, from entropy and mutual details to channel means and the knowledge transmission theorem. eventually, they supply insights into the connections among coding idea and different fields. Many labored examples are given through the ebook, utilizing useful purposes to demonstrate theoretical definitions. workouts also are incorporated, permitting readers to double-check what they've got discovered and achieve glimpses into extra complicated subject matters, making this excellent for somebody who wishes a short advent to the topic

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34). 40 Repetition and Hamming codes This code is called the single parity-check code; see Chapter 2. ♦ In the above exercise, we have introduced the concept of a dual code. The dual code is useful in the sense that once you have an (n, k) linear code with generator matrix G and parity-check matrix H, you immediately get another (n, n − k) linear code for free, simply by reversing the roles of G and H. However, readers should be warned that this is very often not for the purpose of error correction.

Since the scratches are inevitable, it makes no sense to ask the users to keep the disks in perfect condition, or discard them once a perfect read-out from the disk becomes impossible. Therefore, it would be better to have some kind of engineering mechanism to protect the data from being compromised by minor scratches. 1 MP3 stands for MPEG-2 audio layer 3, where MPEG is the abbreviation for moving picture experts group. 32 Repetition and Hamming codes We use error-correcting codes to accomplish this task.

5 Note that in this example the modulus 10 is used although this is not a prime. 46), however, makes sure that every single error can still be detected. The reason why UPC chooses 10 as the modulus is that the check digit should also range from 0 to 9 so that it can easily be encoded by the bar code. 10 For an information source of eight possible outputs, obviously each output can be represented by a binary 3-tuple, say (x1 , x2 , x3 ). 48) 3 to form a legitimate codeword (x1 , x2 , x3 , x4 , x5 , x6 ).

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

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