# Analysis of Video Transmission Capabilities in a Simulated OFDM-Based Supplementary BPL-PLC System
## 3 Materials and Methods
### Transmission Link  
The transmission quality has been investigated in the Matlab/Simulink environment. The simulated model enabled to determine the resulting bit error rate (BER) in case of video files, as shown in Figure 7.  
The principal parameters of the simulated system are described in Table 1.  
Figure 6: Methodology of performing verification measurements for mixed (capacitive–inductive) coupling. Figure 7: Simulated video transmission system. The video content utilized during the study was available in color and therefore split into different streams in the red, green and blue (RGB) model, just before multiplexing, as shown in Figure 8.  
At the beginning, the input file was compressed into smaller blocks of 8 \(\times\) 8 pixels. Next, those blocks were transformed one by one as an image \(f\) of size \([M\times N]\), representing a single frame from the input video file. In the two-dimensional pixel domain (\(x\),\(y\)), it would be expressed as \(f(x\),\(y\)). In order to transform the image in the frequency domain, the 2D discrete cosine transform (DCT) was utilized. Thus, the output image would be given by:  
\[F(m,n)=\frac{2}{\sqrt{MN}}C(m)C(n)\sum_{x=0}^{M-1}\sum_{y=0}^{N-1}f(x,y)cos \frac{(2x+1)m\pi}{2M}cos\frac{(2y+1)n\pi}{2N}, \tag{7}\]  
where:  
\[\left\{ \begin{array}{cc}C(m)=C(n)=\frac{1}{\sqrt{2}}&for\ m=n=0\\ C(m)=C(n)=1&\forall m,n\in C:m,n\ \
eq 0\end{array} \right.. \tag{8}\]  
Such an operation was realized in the transmitting part. In case of the receiving part, a reverse operation, namely, the 2D inverse discrete cosine transform (IDCT), was performed on the image \(F\) in the pixel domain (\(m\),\(n\)). This inverse transformation converted the \(F\) image into the time domain according to:  
\[F(x,y)=\frac{2}{\sqrt{MN}}\sum_{m=0}^{M-1}\sum_{m=0}^{N-1}C(m)C(n)f(m,n)cos \frac{(2x+1)m\pi}{2M}cos\frac{(2y+1)n\pi}{2N}, \tag{9}\]  
where:  
\[\left\{ \begin{array}{cc}C(m)=C(n)=\frac{1}{\sqrt{2}}&for\ m=n=0\\ C(m)=C(n)=1&\forall m,n\in C:m,n\ \
eq 0\end{array} \right.. \tag{10}\]  
The compressed channels were multiplexed in order to adapt them into a single transmission medium. Such an operation was required so that the forward error correction (FEC) could be performed, just like in a typical terrestrial video broadcasting system [34; 35]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Description** \\ \hline Resolution and refresh rate & 480 \(\times\) 270, 24 FPS \\ Color model & RGB \\ Compression algorithm & 8 \(\times\) 8, DCT, quantization, lossless compression \\  Protection coding & FEC 3/4 \\ Modulation and coding scheme & (BCH + LDPC 3/4) \\ No. of subcarriers & 81 \\ Carrier spacing & 42 kHz \\ Channel bandwidth & 3.4 MHz \\ Channel model & AWGN \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of the simulated video transmission system. Figure 8: Handling of the video content in the RGB mode. In our case, the FEC encoding was identical to that used in the well-known DVB-T standard [36]. According to available literature, this standard utilizes a combination of the Bose-Chaudhuri-Hocquenghem (BCH) code, which is a subclass of cyclic error correction codes build over finite bodies with linear low-density parity check (LDPC) correction coding. The simulated FEC encoder had the following parameters, as described in Table 2.  
First, the binary message of length \(k_{bch}\) was encoded with the \(n_{bch}\) BCH-bit code word. Then, the BCH code word \(k_{ldpc}\) equal to \(n_{bch}\) was coded into an \(n_{ldpc}\) LDPC-bit code word. The code word \(n_{ldpc}\) was equal to 64,800 bits in length. The lengths of \(k_{bch}\) and \(k_{ldpc}\) were variable and depended on the code rate. In case of our system, the efficiency was equal to three-fourths. Later on, the data were subjected to the interleaving mechanism. The designed interleaver transformed the data according to a random permutation based on a fixed initial state. The permutation table was selected randomly using the specified input parameter.