By Stefan M. Moser
This easy-to-read advisor presents a concise advent to the engineering history of recent communique platforms, from cell phones to facts compression and garage. heritage arithmetic and particular engineering strategies 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 commence with many useful 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 info to channel capability and the data transmission theorem. eventually, they supply insights into the connections among coding concept and different fields. Many labored examples are given during the publication, utilizing sensible functions to demonstrate theoretical definitions. routines also are incorporated, permitting readers to double-check what they've got discovered and achieve glimpses into extra complicated issues, making this ideal for somebody who wishes a brief advent to the topic
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Extra resources for A Student’s Guide to Coding and Information Theory
A bijection, since if it were not a bijection, it would not be possible to recover the original data. On the other hand, because of the bijection, when the stored data stream x is corrupted, it is impossible to recover the original s. Therefore, we see that the protection process (henceforth we will refer to it as an encoding process) must be an injection, meaning x must have length larger than k, say n, so that when x is corrupted, there is a chance that s may be recovered by using the extra (n − k) bits we have used for storing extra information.
For example, assume codeword x = (0 1 1 0 1 0 0) was written onto the CD, but due to an unknown one-bit error the read-out shows (0 1 1 1 1 0 0). 2. Because of the unknown onebit error, we see that • the number of 1s in circle I is 1, an odd number, and a warning (bold circle) is shown; • the number of 1s in circle II is 3, an odd number, and a warning (bold circle) is shown; • the number of 1s in circle III is 2, an even number, so no warning (normal circle) is given. From these three circles we can conclude that the error must not lie in circle III, but lies in both circles I and II.
Denote by x the original bit in the th message position, ∀ 1 ≤ ≤ n − 1, and let xn be the parity-check bit. 1). Note that here (and for the remainder of this book) we omit “mod 2” and implicitly assume it everywhere. Let y be the channel output corresponding to x , ∀ 1 ≤ ≤ n. At the receiver, we firstly count the number of 1s in the received sequence y. e. 27) =1 this indicates that at least one error has occurred. 28) and hence the resulting even-parity codeword (x1 , x2 , x3 , x4 , x5 ) is (0 1 1 1 1).