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

By Yuan Jing

ISBN-10: 1608070891

ISBN-13: 9781608070893

This functional source offers engineers with a finished knowing of errors regulate coding, a vital and broadly utilized zone in sleek electronic communications. The objective of blunders regulate coding is to encode info in this type of means that no matter if the channel (or garage medium) introduces error, the receiver can right the blunders and get better the unique transmitted details. This ebook comprises the main priceless smooth and vintage codes, together with block, Reed Solomon, convolutional, rapid, and LDPC codes. execs locate transparent tips on code development, deciphering algorithms, and blunder correcting performances. additionally, this certain e-book introduces laptop simulations integrally to aid readers grasp key recommendations. together with a better half DVD with MATLAB courses and supported with over 540 equations, this hands-on reference presents an in-depth remedy of quite a lot of useful implementation matters. DVD is integrated! It includes rigorously designed MATLAB courses that practitioners can observe to their tasks within the box.

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So it is a subspace of V2(3). 1 Definition A field with a finite number of elements is a finite field, or Galois field, in memory of its discoverer É. Galois. A Galois field of order q is denoted by GF(q). The Galois field is extensively used in coding theory. 3 is a Galois field. If the order of a Galois field is a prime p, then the field is called the prime field. Evidently the binary field is moreover a prime field with p = 2. For any Galois field GF(q), there exists a smallest positive integer l such that: 1� + 1 +�� + 1� = 0 λ 1's The integer l is called the characteristic of the field.

Consequently, we can also say that an extension field is built on a primitive polynomial. 1 We use MATLAB to verify that 1 + X + X 3 is a primitive polynomial; that is, it divides X 7 - 1 but not X n - 1 for 0 < n < 7. >> p1 = [1 1 0 1]; % polynomial 1 + x + x^3 >> p2 = [1 0 0 0 0 0 0 1]; % polynomial 1 + x^7 >> p3 = [1 0 0 0 0 0 1]; % polynomial 1 + x^6 >> % for polynomials over GF(2), x^7 – 1 = 1 + x^7, >> % x^6 – 1 = 1 + x^6, ... >> [q,r] = gfdeconv(p2,p1); % (1 + x^7)/(1 + X + x^3) >> % q: quotient, r: remainder >> r r = 0 >> [q,r] = gfdeconv(p3, p1); % (1 + x^6)/(1 + x + x^3) >> r r = 0 0 1 So, 1 + X + X 3 divides X 7 - 1 but not X 6 - 1.

3. Multiplication × is distributive over addition +; that is, a × (b + c) = a × b + a × c, where a, b, and c are any three elements in F. The identity element with respect to addition, denoted by 0, is called the zero element, and the identity element with respect to multiplication, denoted by 1, is called the unit element. The total number of elements in a field is referred to as the order of the field. 4 The set {0, 1} with the modulo-2 addition Å and the modulo-2 multiplication Ä defined in the previous two examples forms the binary field.

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A practical guide to error-control coding using Matlab by Yuan Jing

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