By Yuan Jing

ISBN-10: 1608070891

ISBN-13: 9781608070893

This functional source presents engineers with a entire figuring out of errors regulate coding, a vital and broadly utilized sector in glossy electronic communications. The objective of errors keep watch over coding is to encode details in the sort of means that no matter if the channel (or garage medium) introduces mistakes, the receiver can right the mistakes and get better the unique transmitted info. This e-book contains the main invaluable sleek and vintage codes, together with block, Reed Solomon, convolutional, rapid, and LDPC codes. pros locate transparent assistance on code development, deciphering algorithms, and mistake correcting performances. furthermore, this particular ebook introduces machine simulations integrally to assist readers grasp key techniques. together with a spouse DVD with MATLAB courses and supported with over 540 equations, this hands-on reference presents an in-depth therapy of quite a lot of sensible implementation concerns. DVD is integrated! It includes conscientiously designed MATLAB courses that practitioners can follow to their initiatives within the box.

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**Additional resources for A practical guide to error-control coding using Matlab**

**Example text**

For every a Î G, there exists an element a -1 Î G such that a * a -1 = e, where a -1 is called the inverse of a. The group is denoted by áG, *ñ. The identity of a group is unique, and so is the inverse of an element in a group. 1 Let G Î {1, 0} and the operation Å be defined as: Å 0 1 0 0 1 1 1 0 The operation Å is called the modulo-2 addition (or the exclusive-or operation, XOR). áG, Åñ forms a group. From the preceding table we can easily verify that Å is associative. The element 0 is the identity element because 0 Å 1 = 1 Å 0 = 1, and 0 Å 0 = 0.

Note that this code is a systematic code. The first four MSBs of the codewords are the message bits. The remaining three bits are the parity bits. 1 Codewords of a (7,4) Block Code Message Word (LSB … MSB) Codeword (LSB … MSB) m 0 = (0000) c 0 = (0000000) m 1 = (1000) c 1 = (1101000) m 2 = (0100) c 2 = (0110100) m 3 = (1100) c 3 = (1011100) m 4 = (0010) c 4 = (1110010) m 5 = (1010) c 5 = (0011010) m 6 = (0110) c 6 = (1000110) m 7 = (1110) c 7 = (0101110) m 8 = (0001) c 8 = (1010001) m 9 = (1001) c 9 = (0111001) m 10 = (0101) c 10 = (1100101) m 11 = (1101) c 11 = (0001101) m 12 = (0011) c 12 = (0100011) m 13 = (1011) c 13 = (1001011) m 14 = (0111) c 14 = (0010111) m 15 = (1111) c 15 = (1111111) Note: LSB = least significant bit; MSB = most significant bit.

For instance, polynomial 1 + X + X 3 is an irreducible polynomial over GF(2), but X + X 3 is not because (X + X 3)/X = 1 + X 2. Irreducible polynomials have an important feature, that is, any irreducible polynomial of degree m dim 3 vides X p -1 -1[5, p. 207]. This is easy to verify. An irreducible polynomial j(X ) of degree m is said to be primitive if the smallest positive integer n for which j(X ) divides X n - 1 is n = pm - 1. Interestingly, the roots of an mth degree primitive polynomial j(X ) over GF( p) are primitive elements of some extension field GF( pm) [5, p.