By Stefan M. Moser
This easy-to-read consultant presents a concise advent to the engineering heritage of recent communique platforms, from cell phones to information compression and garage. history arithmetic and particular engineering suggestions are stored to a minimal in order that just a uncomplicated 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 conception, from entropy and mutual details to channel means and the knowledge transmission theorem. eventually, they supply insights into the connections among coding conception and different fields. Many labored examples are given in the course of the publication, utilizing functional purposes to demonstrate theoretical definitions. routines also are integrated, allowing readers to double-check what they've got realized and achieve glimpses into extra complicated issues, making this ideal for an individual who wishes a brief advent to the topic
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Additional resources for A Student’s Guide to Coding and Information Theory
For example, the Hamming distance between (1 0 1 1 1 0 0) and (0 1 1 1 0 0 1) is 4 since x differs from x in the first, second, fifth, and seventh positions. Equivalently, you can compute (1 0 1 1 1 0 0) + (0 1 1 1 0 0 1) = (1 1 0 0 1 0 1). Then the condition given in Exer? 2, namely, x = x is equivalent to x + x = 0 for = 1, 2, . . , 7, shows the distance is 4 since there are four 1s appearing in the sum (1 1 0 0 1 0 1). Note that the number of ones in a binary vector is called the Hamming weight of the vector.
1. 20) that is smaller than the original p. 3 Prove 3p2 (1 − p) + p3 < p for p ∈ (0, 1/2). 1 is obtained under the assumption of Pr[s = 0] = Pr[s = 1] = 1/2. What if Pr[s = 0] = 0 and Pr[s = 1] = 1? Reconstruct the table for this case and conclude that Pr(Uncorrectable error) = 0. Then rethink whether you need error protection and correction in this case. ♦ To summarize this section, below we give a formal definition of an errorcorrecting code. 5 A code C is said to be an (n, k) error-correcting code if it is a scheme of mapping k bits into n bits, and we say C has code rate R = k/n.
Storing CDs and DVDs inevitably causes small scratches on the disk surface. These scratches impair the disk surface and create some kind of lens effect so that the laser reader might not be able to retrieve the original information correctly. When this happens, the stored files are corrupted and can no longer be used. 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.