A = imread('krabi1.bmp','BMP'); %read in the image A_shrunk = imresize(A,0.2); % we’ll reduce the resolution, as otherwise the file size is too large imshow(A_shrunk) % displays the shrunken image Bs = reshape(A_shrunk,[388*518*3,1,1]); % resizes this image from a pixel array of three colours to a one-dimensional data stream C = de2bi(double(Bs)); % converts these values to binary representation % You can then resize this array to a linear, one-dimensional array. % this data stream C is then what you can communicate over your channel. % recover the image from the binary sequence BS_rec = uint8(bi2de(C)); % convert bits to pixel values. A_rec = reshape(BS_rec,[388,518,3]); % reshape back to a coloured pixel array. imshow(A_rec) % display the recovered image. Explore the pskmod and pskdemod commands in MATLAB. Use these to modulate and demodulate the binary sequence into a binary PSK signal. (Hint: the command should be something like D = pskmod(C,2). Display a part of this signal, and explain carefully how we have represented this signal in MATLAB, and how it differs from the analysis we performed in Part A. Transmit this signal through an AWGN channel using the awgn() function for a range of signal to noise ratios. Demodulate and comment on the effect of the noise on the image. A suitable range of signal to noise ratios is –0.5dB to 5 dB. The bit error rate refers to the fraction of bits that are received in error. This can also be interpreted as the probability that a bit is received in error. Calculate the bit error rate (BER) for the signal to noise ratios you used above. Comment on the correlation between BER and perceptual image quality. Now apply channel coding to the transmitted data sequence. Use encode(msg,7,4,’hamming’), encode(msg,15,7,’bch’), and convenc, following the example listed in the help window (recall, in MATLAB type “help convenc” to obtain the help information for that command. For each of these codes, study how the code can reduce the BER and improve image quality for each SNR you studied above.

这是一个关于数字图像处理和通信的问题，需要一些MATLAB知识。下面是对问题的回答：

1. 读入并压缩图像

首先，使用`imread`函数读入一张图片，并使用`imresize`函数将图片压缩到原来的20%大小：

A = imread('krabi1.bmp', 'BMP');
A_shrunk = imresize(A, 0.2);

2. 将图像转换为一维数据流

将压缩后的图像重新排列为一维数据流，以便进行数字通信。使用`reshape`函数将3通道的像素矩阵转换为一维列向量，并使用`de2bi`函数将像素值转换为二进制表示：

Bs = reshape(A_shrunk, [388*518*3, 1, 1]);
C = de2bi(double(Bs));

3. 二进制PSK调制

使用`pskmod`函数将二进制数据流进行相位调制，生成二进制PSK信号。例如，调制成二进制PSK2：

D = pskmod(C, 2);

4. 加入高斯白噪声

使用`awgn`函数将二进制PSK信号加入高斯白噪声，模拟通信信道的影响。例如，将信噪比设置为0dB：

noisy_D = awgn(D, 0, 'measured');

5. 二进制PSK解调

使用`pskdemod`函数将接收到的二进制PSK信号解调回二进制数据流：

rec_C = pskdemod(noisy_D, 2);

6. 解码并恢复图像

使用`bi2de`函数将二进制数据流转换为像素值，然后使用`reshape`函数将像素值重新排列为3通道的像素矩阵，最后使用`imshow`函数显示恢复后的图像：

rec_Bs = uint8(bi2de(rec_C));
A_rec = reshape(rec_Bs, [388, 518, 3]);
imshow(A_rec);

7. 计算误码率

使用`biterr`函数计算解调后的数据流和原始数据流之间的误码率，并根据不同信噪比的误码率绘制误码率曲线：

ber = zeros(1, length(snr));
for i = 1:length(snr)
    noisy_D = awgn(D, snr(i), 'measured');
    rec_C = pskdemod(noisy_D, 2);
    ber(i) = biterr(C, rec_C) / length(C);
end
semilogy(snr, ber);

8. 应用通道编码

使用`encode`函数对二进制数据流进行通道编码，对比不同编码方案的误码率曲线和图像质量：

% Hamming(7,4)编码
hamming_encoded = encode(C, 7, 4, 'hamming');
hamming_D = pskmod(hamming_encoded, 2);
hamming_noisy_D = awgn(hamming_D, snr(i), 'measured');
hamming_rec_C = pskdemod(hamming_noisy_D, 2);
hamming_rec_Bs = uint8(bi2de(hamming_rec_C));
hamming_A_rec = reshape(hamming_rec_Bs, [388, 518, 3]);
hamming_ber(i) = biterr(C, hamming_rec_C) / length(C);

% BCH(15,7)编码
bch_encoded = encode(C, 15, 7, 'bch');
bch_D = pskmod(bch_encoded, 2);
bch_noisy_D = awgn(bch_D, snr(i), 'measured');
bch_rec_C = pskdemod(bch_noisy_D, 2);
bch_rec_Bs = uint8(bi2de(bch_rec_C));
bch_A_rec = reshape(bch_rec_Bs, [388, 518, 3]);
bch_ber(i) = biterr(C, bch_rec_C) / length(C);

% 卷积编码
trellis = poly2trellis(7, [171 133]);
conv_encoded = convenc(C, trellis);
conv_D = pskmod(conv_encoded, 2);
conv_noisy_D = awgn(conv_D, snr(i), 'measured');
conv_rec_D = pskdemod(conv_noisy_D, 2);
conv_rec_C = vitdec(conv_rec_D, trellis, 15, 'trunc', 'hard');
conv_rec_Bs = uint8(bi2de(conv_rec_C));
conv_A_rec = reshape(conv_rec_Bs, [388, 518, 3]);
conv_ber(i) = biterr(C, conv_rec_C) / length(C);

需要注意的是，以上代码仅供参考，具体实现还需要根据实际情况进行调整。