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Channel Coding Theory Assignment

Part I 1) Use the 'GF' function in MATLAB to generate the elements of GF(16) ={0,1,2,..15}

using the primitive polynomial X4+ X + 1. Do the following operation 11 X 12, 5 + 6, 9 + 15

2) For double-error correcting BCH code with n =15, write a MATLAB function script that can encode information vector.

3) Write a MATLAB function that convert vector in GF(15) to its frequency domain. You are restricted to use ‘polyval’ function to find the spectral components. (show for you’re the generator polynomial and the code-words generated in part 2 have 4 consecutive zeros in its spectral components).

4) Write a MATLAB script to use Euclid’s algorithm to find the error locator

polynomials. By using function ‘roots’ find the location of errors and hence correct it. (if the roots does not exist, then take the first k bits as the message).

Consider single, double and triple errors in one of the code words achieved in 2. Try now to decode them by using the scripts you have written. Part II We want to use Monte-Carlo simulation to see the performance of BCH (15,7) code over additive white Gaussian noise channel.

1) Consider that Signal to Noise Ratio (SNR) varies from 1 to 40 at each SNR do the following

2) We will consider a stream of 10,000 bits of information generated by the following scripts

Temp = rand If (temp < 0.5) Data = -1; else Data = 1; End If you did manage to do part I, You can use the built-in functions in MATLAB to encode and decode the message . 3) Plot the Bit Error Rate (BER) against SNR (dB).

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Part III Repeat for n =15 and single-error correction BCH code. Part IV Repeat part two for Hamming (15,11) Plot graphs from II, III and IV in the same graph. Deliverable: 1) A full documented report contains all your results. 2) Simulink representations for part II,III,IV (bonus) 3) Soft copy of your MATLAB scripts 4) Any plagiarism from any source won't be tolerated. Sever punishment will be

the consequence.