By Stefan M. Moser
This easy-to-read consultant presents a concise advent to the engineering historical past of recent verbal exchange structures, from cell phones to info compression and garage. historical past arithmetic and particular engineering recommendations are stored to a minimal in order that just a simple 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 thought, from entropy and mutual details to channel potential and the knowledge transmission theorem. eventually, they supply insights into the connections among coding idea and different fields. Many labored examples are given in the course of the booklet, utilizing functional purposes to demonstrate theoretical definitions. workouts 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 short creation to the topic
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Additional info for A Student's Guide to Coding and Information Theory
E. 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.
The use of R-S codes as a means of error correction for CDs was suggested by Jack van Lint (1932–2004) while he was employed at Philips Labs in 1979. Two consecutive R-S codes are used in serial in a CD. These two R-S codes operate in bytes (B) instead of bits (1 B = 8 bits). The first R-S code takes in 24 B of raw data and encodes them into a codeword of length 28 B. After this, another mechanism called interleaver would take 28 such encoded codewords, each 28 B long, and then permute the overall 282 = 784 B of data symbols.
The only difference between binary and usual additions is the case of 1 + 1. Usual addition would say 1 + 1 = 2. But since we are working with modulo2 addition, meaning the sum is taken as the remainder when divided by 2, the remainder of 2 divided by 2 equals 0, hence we have 1 + 1 = 0 in binary arithmetics. 2) 1 = 0 − 1. Further, it is interesting to note that the above equalities also hold if we replace “−” by “+”. Then we realize that, in binary, subtraction is the same as addition. This is because the remainder of −1 divided by 2 equals 1, meaning −1 is considered the same as 1 in binary.
A Student's Guide to Coding and Information Theory by Stefan M. Moser