By Stefan M. Moser
This easy-to-read consultant presents a concise creation to the engineering historical past of recent conversation platforms, from cell phones to info compression and garage. history arithmetic and particular engineering recommendations are saved to a minimal in order that just a uncomplicated wisdom of high-school arithmetic is required to appreciate the cloth lined. 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 idea, from entropy and mutual details to channel means and the data 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. workouts also are incorporated, allowing readers to double-check what they've got realized and achieve glimpses into extra complicated themes, 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
5 occurs, the error will not be detected due to the all-zero check sum. 4 Could you repeat the above process of encoding for the case of L = 16? Also, show that the resulting code can detect all the bursts of length at most 16. 5 Can you show that the error might not be detected if there is more than one burst, even if each burst is of length no larger than L? 6 Alphabet plus number codes – weighted codes The codes we have discussed so far were all designed with respect to a simple form of “white noise” that causes some bits to be flipped.
20) Denote by ξ the greatest integer not larger than ξ . We have2 n/2 Pr(An even number of errors) = n 2 ∑ =0 p2 (1 − p)n−2 1 + (1 − 2p)n . 2 The probability of an odd number of errors is 1 minus this number. 23) and (n−1)/2 ∑ =0 2 n p2 2 +1 +1 (1 − p)n−2 −1 = 1 − (1 − 2p)n 2 Note that zero errors also counts as an even number of errors here. 3 Single parity-check code 17 by induction on n? Hint: Note that n+1 n n = + k k k−1 for n, k ≥ 1. 3 Single parity-check code The simplest way of encoding a binary message to make it error-detectable is to count the number of 1s in the message, and then append a final binary digit chosen so that the entire message has an even number of 1s in it.
North-Holland, Amsterdam, 1977. [Wic94] Stephen B. Wicker, Error Control Systems for Digital Communication and Storage. Prentice Hall, Englewood Cliffs, NJ, 1994. 3 Repetition and Hamming codes The theory of error-correcting codes comes from the need to protect information from corruption during transmission or storage. Take your CD or DVD as an example. Usually, you might convert your music into MP3 files1 for storage. e. they use fewer binary digits (bits) compared with the original format on CD.