By Stefan M. Moser
This easy-to-read advisor presents a concise advent to the engineering history of recent verbal exchange structures, from cellphones to info compression and garage. heritage arithmetic and particular engineering innovations are saved to a minimal in order that just a uncomplicated wisdom of high-school arithmetic is required to appreciate the cloth coated. The authors start with many useful purposes in coding, together with the repetition code, the Hamming code and the Huffman code. They then clarify the corresponding info conception, from entropy and mutual info to channel ability and the data transmission theorem. eventually, they supply insights into the connections among coding thought and different fields. Many labored examples are given in the course of the publication, utilizing sensible purposes to demonstrate theoretical definitions. workouts also are integrated, permitting readers to double-check what they've got discovered and achieve glimpses into extra complex issues, making this ideal for someone who wishes a short advent to the topic
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Additional resources for A Student’s Guide to Coding and Information Theory
9 The Universal Product Code (UPC) is a 12-digit single paritycheck code employed on the bar codes of most merchandise to ensure reliability in scanning. 11 Checking the ISBN number 0 – 5218 – 4868 – 7 Sum 0 5 2 1 8 4 8 6 8 7 0 5 7 8 16 20 28 34 42 49 Sum of sum 0 5 12 20 36 56 84 118 160 209 = 11 × 19 ≡ 0 mod 11 where the last digit is the parity-check digit. Denote the digits as x1 , x2 , . . , x12 . 46) is a multiple5 of 10. In this case, 3(0 + 6 + 0 + 2 + 1 + 5) + (3 + 0 + 0 + 9 + 4 + 2) = 60.
4(b) (you might want to think of them as highdimensional balls), each with radius R = 1, centered at x and x , respectively, these two spheres would not overlap and must be well-separated. Points within the x-sphere represent the read-outs that are at a distance of at most 1 from x. In other words, the points within the x-sphere are either x or x with a one-bit error. 4 Geometry of x = x in the (7, 4) Hamming code with Hamming distance 3. If we draw a sphere with radius R = 1 centered at each codeword of the (7, 4) Hamming code, there will be 16 nonoverlapping spheres since there are 16 codewords and every pair of distinct codewords is separated by a distance of at least 3.
The same holds for the other write-in of (1 1 1). Thus we say that the three-times repetition code is a singleerror-correcting code, meaning the code is able to correct all possible one-bit errors. 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.
A Student’s Guide to Coding and Information Theory by Stefan M. Moser