Write MATLAB code for $(1)$ Simulate transmission of the lenna image $($attached$)$ using BPSK$.$ For this purpose, the pixel values have to be converted to bits, then modulated and transmitted and finally detected. Do this experiment at a low SNR Eb$/$No of $0$ dB and also at a high SNR of $4$ dB$.$ Print the images. Compare and comment.

$(2)$ Employ a linear error detection code $($only detection and no correction$)$ and transmit using BPSK again. The code can be your choice, and you can pick any code from the book but should not be too trivial, say a $(2,1)$ code or a repetition code. Consider first $0$ dB SNR$.$ In this case, assume that when a packet is received in error, the detector makes a retransmission request. Count the number of re$-$transmission requests at $0$ dB$,2$ dB$,4$ dB$,6$ dB$,8$ dB and $10$ dB SNR respectively until there is no error. Plot the number of re$-$transmission requests against the SNR values.

$(3)$ Use an error correction code $($of your choice$)$ using syndrome look up table and correct errors directly at the receiver without sending any retransmission request. The code cannot be a too simple code, for example, $(3,1)$ or $(4,2)$ etc. Show images at $0$ dB and $4$ dB SNR after employing error correction. Give comments comparing results with no error correction and results with error correction.