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 heritage of contemporary conversation platforms, from cell phones to info compression and garage. historical past arithmetic and particular engineering options are saved to a minimal in order that just a simple wisdom of high-school arithmetic is required to appreciate the fabric coated. The authors start with many functional purposes in coding, together with the repetition code, the Hamming code and the Huffman code. They then clarify the corresponding details concept, from entropy and mutual details to channel skill and the knowledge transmission theorem. ultimately, they supply insights into the connections among coding idea and different fields. Many labored examples are given during the ebook, utilizing useful functions to demonstrate theoretical definitions. routines also are integrated, permitting readers to double-check what they've got discovered and achieve glimpses into extra complex subject matters, making this ideal for somebody who wishes a brief creation to the topic

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

**Sample text**

This corresponds to almost half of the storage capacity of a DVD! Therefore, we see that while the three-times repetition code is able to provide some error protection, it is highly inefficient in terms of rate. In general, we would like the rate R = k/n to be as close to 1 as possible so that wastage of storage space is kept to a minimum. 1 Some historical background The problem of finding efficient error-correcting schemes, but of a much smaller scale, bothered Richard Wesley Hamming (1915–1998) while he was employed by Bell Telephone Laboratory (Bell Labs) in the late 1940s.

We can sum these sums again in the same way to obtain the desired weighted sum. 6 We assign a distinct number from {0, 1, 2, . . , 36} to each symbol in the combined alphabet/number set in the following way: “0” = 0, “1” = 1, “2” = 2, . . , “9” = 9, “A” = 10, “B” = 11, “C” = 12, . . , “Z” = 35, and “space” = 36. Then we encode 3B 8. 7 and obtain a weighted sum of 183. Since 183 mod 37 = 35 and 35 + 2 is divisible by 37, it follows that the appended check digit should be “2” = 2. 7 Progressive digiting for the example of “3B 8”: we need to add “2” = 2 as a check-digit to make sure that the weighted sum divides 37 “3” “B” “space” “8” Check-digit = = = = = 3 11 36 8 ??

Based on the above, verify the following: (a) The dual code C ⊥ of the three-times repetition code is a (3, 2) linear code with rate R = 2/3, and (b) C ⊥ is a 1-error-detecting code. 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.

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

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