(Solved): code the following task using MATLAB please Part One: Design and evaluation ...

code the following task using MATLAB please

???????

Part One: Design and evaluation of Hamming Code. - Design a \( (7,4) \) Hamming encoder and decoder - Generate uniformly distributed information bits using \{rand\} in Matlab. - Encode the information bits using the \( (7,4) \) Hamming encoder - Map the resulting codeword bits to a BPSK (Binary phase shift keying symbols). Map bit one to symbol \( +1 \) and bit zero to symbol \( -1 \). - Transmit the modulated codeword over the AWGN channel. Use the following model: \[ y=\sqrt{R \gamma} x+\eta \] where: \( y \) is the received symbol \( \mathrm{R} \) is the code rate \( \gamma \) is the information signal to noise ratio (SNR) (scalar value not in \( \mathrm{dB} \) ) \( x \) is the transmitted BPSK symbol of Energy one \( \eta \) the AWGN random variable of power one. use \{randn\} in Matlab - At the receiver, - Make a hard decision on the received symbols: - If \( y \geq 0 \rightarrow \tilde{x}=+1 \) - If \( \mathrm{y} \leq 0 \rightarrow \tilde{x}=-1 \) - Demodulate the received symbols, convert from symbols to bits. - Decode the received bits using syndrome decoding of the Hamming code. - Compare the decoded information bits with the transmitted bits and count the errors. - Repeat the simulation for total number of 100000 information bits. Keep counting the number of errors. - When the loop ends, calculate the bit error rate (BER) at the operated \( \operatorname{SNR}\left(\gamma_{d B}\right) \) \[ B E R\left(\gamma_{d B}\right)=\frac{\text { number of errors }}{\text { total number of information }} \] - Now, you have one point as a result of the simulation which is \( \left(\gamma_{d B}, B E R\left(\gamma_{d B}\right)\right) \). - Repeat the simulation for \( \gamma_{d B}=0: 2: \gamma_{\max } \), where \( \gamma_{\max } \) gives a BER around \( 10^{-4} \). - Compare the BER of the uncoded BPSK and the coded system. Use \{semilogy\} in Matlab. Plot the two outputs on the same figure. \{hint: for the uncoded case, \( R=1 \) and remove the encoder/ decoder \( \} \)