Download e-book for kindle: A practical guide to error-control coding using Matlab by Yuan Jing

By Yuan Jing

This sensible source offers engineers with a complete knowing of blunders keep watch over coding, a necessary and largely utilized region in sleek electronic communications. The objective of errors keep watch over coding is to encode info in the sort of means that no matter if the channel (or garage medium) introduces error, the receiver can right the mistakes and get well the unique transmitted info. This ebook comprises the main necessary sleek and vintage codes, together with block, Reed Solomon, convolutional, rapid, and LDPC codes. pros locate transparent information on code building, interpreting algorithms, and blunder correcting performances. furthermore, this distinctive ebook introduces desktop simulations integrally to assist readers grasp key ideas. together with a spouse DVD with MATLAB courses and supported with over 540 equations, this hands-on reference presents an in-depth therapy of a variety of sensible implementation matters. DVD is incorporated! It includes rigorously designed MATLAB courses that practitioners can practice to their initiatives within the box.

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If power representation is used, the product is obtained as: a 3 × a 5 = a (3 + 5)mod 2 3_1 = a 36 A Practical Guide to Error-Control Coding Using MATLAB® On the other hand, if polynomial representation is used, the multiplication should be performed as follows: a 3 × a 5 = (1 + X ) × (1 + X + X 2) mod (1 + X + X 3)½X = a = 1 +X 3 mod (1 + X + X 3)½X = a = a where 1 + X + X 3 is the primitive polynomial that we used to construct the field. 6 MATLAB contains a set of functions dedicated to Galois field arithmetic such as gfadd, gfsub, and gfmul.

The characteristic of GF(2) is 2 because 1 Å 1 = 0. For a prime field GF(p), the characteristic is p. It can be shown that the characteristic of any Galois field must be a prime [4, p. 35]. The preceding definition of a characteristic implies that, for any integer 0 < k < l, 1� + 1 +�� + 1� ¹ 0 k 1's The sum is in fact distinct with different k, and these l distinct sums, 1,(1 + 1),�,(1 � + 1 +�� + 1)� , form a field GF(l) under addition and multiplicaλ 1's tion. The resulting field GF(l) is a subfield of GF(q).

4. 13 we can see that the LFSR is connected in such a way that it becomes the so-called maximum-length LFSR and is able to exhaust all 2m - 1 nonzero elements in the field (although in the example we were lucky to obtain the inverse before exhausting all the elements). Also, each shift of the LFSR is equivalent to multiplying its content by X followed by modulo-j(X ). One issue associated with the preceding technique is that the number of shifts needed for different elements is different. This may cause some problem when interfacing with other circuit blocks.

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