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

By Yuan Jing

This sensible source presents engineers with a complete figuring out of mistakes keep watch over coding, a necessary and largely utilized quarter in sleek electronic communications. The aim of blunders keep watch over coding is to encode details in this kind of method that whether the channel (or garage medium) introduces blunders, the receiver can right the error and recuperate the unique transmitted info. This e-book comprises the main necessary glossy and vintage codes, together with block, Reed Solomon, convolutional, faster, and LDPC codes. execs locate transparent suggestions on code development, interpreting algorithms, and mistake correcting performances. furthermore, this specified ebook introduces desktop simulations integrally to assist readers grasp key thoughts. together with a spouse DVD with MATLAB courses and supported with over 540 equations, this hands-on reference offers an in-depth therapy of quite a lot of useful implementation matters. DVD is incorporated! It comprises conscientiously designed MATLAB courses that practitioners can observe to their initiatives within the box.

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Reduction modulo the primitive polynomial. The above implementation approach is often not favored in high-speed design because it is a multiple-cycle operation and the circuit thus must be clocked at a much higher frequency than the data rate. However, given the primitive polynomial j(X ) = j0 + j1X + ... + jm X m, it is possible to complete the second step off-line. Let u(X ) = u0 + u1 X + ... + um-1 X m-1, v(X ) = v0 + v1X + ... + vm –1 X m –1. 17) k = m, m + 1,�,2m - 2 38 A Practical Guide to Error-Control Coding Using MATLAB® Since the primitive polynomial j(X ) is known, terms X m mod j(X ), X mod j(X ), ...

Let u = (u0 u1 u2 ... un-1) and v = (v0 v1 v2 ... vn-1) be two elements of V2(n). 1) where ui + vi is carried out as modulo-2 addition (XOR). 2) where aui is performed as modulo-2 multiplication (AND). The all-zero vector 0 = (000 ... 5 For n = 3, the vector space V2(3) has the following eight vector elements: (000), (001), (010), (011), (100), (101), (110), (111), 24 A Practical Guide to Error-Control Coding Using MATLAB® Pick any two vectors, say, (010) and (100). We then have: (010) + (100) = (0 + 1 1 + 0 0 + 0) = (110), which is also an element in V2(3).

The inverse of 0 is 1, the inverse of 1 is 0. G is closed under Ä. áG, Äñ is communicative, too. Brief Introduction to Abstract Algebra 21 The number of elements in a group is the order of the group. A group of finite order is called the finite group. Obviously áG, Åñ and áG, Äñ are both finite groups. Let G ¢ be the subset of G. áG ¢,* ñ is a subgroup of áG,* ñ if and only if áG ¢,* ñ is itself a group. The following theory, Lagrange’s theorem, applies to a group and its subgroup [4]: If áG,* ñ is a finite group of order n, and áG ¢,* ñ is áG,* ñ’s subgroup of order m, then m divides n (in other words, n/m has no remainder).

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