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A Student's Guide to Coding and Information Theory - download pdf or read online

By Stefan M. Moser

This easy-to-read advisor offers a concise creation to the engineering historical past of recent verbal exchange structures, from cellphones to information 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 fabric lined. The authors commence with many sensible functions in coding, together with the repetition code, the Hamming code and the Huffman code. They then clarify the corresponding info concept, from entropy and mutual info to channel skill and the data 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 e-book, utilizing sensible functions to demonstrate theoretical definitions. workouts also are incorporated, permitting readers to double-check what they've got realized and achieve glimpses into extra complex subject matters, making this ideal for a person who wishes a brief advent to the topic

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That is, show that for any a, b, c ∈ {0, 1} we have a + b + c = (a + b) + c = a + (b + c) (additive associative law), a × b × c = (a × b) × c = a × (b × c) (multiplicative associative law), a × (b + c) = (a × b) + (a × c) (distributive law). ♦ ? 2 In this chapter, we will use the notation = to denote a conditional equality, by which we mean that we are unsure whether the equality ? holds. Show that the condition of a = b in binary is the same as a + b = 0. 2 Three-times repetition code A binary digit (or bit in short) s is to be stored on CD, but it could be corrupted for some reason during read-out.

Let us work through some examples in order to understand the question better. 18 The (7, 4) Hamming code has 16 codewords, hence 16 spheres with radius 1, since the code is 1-error-correcting. • The codewords have length 7, with a binary value in each coordinate. 9 = 1. 50 Repetition and Hamming codes the number of possible length-7 binary tuples is 27 = 128, meaning there are 128 points in this 7-dimensional binary space. • Each codeword of the Hamming code is surrounded by a sphere with radius 1.

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 ?? 8 Checking the encoded message “3B 82” 3 B “space” 8 2 3×5 11 × 4 36 × 3 8×2 2×1 = = = = = 15 44 108 16 2 Sum = 185 = 37 × 5 ≡ 0 mod 37 The encoded message is therefore given by 3B 82.

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