## 3 Dependable Wireless System
### Shortened Code  
The definitions of terms and symbols used in Section 3.2 are listed in Table 1.  
We propose to adopt shortened code [8] as the FEC code. Figure 2 shows the encoding procedure of \((n-m,k-m)\) shortened code. The unencoded bits are encoded with \((n,k)\) code, where \(k\) is the unencoded bit length, \(n\) is the codeword length. The unencoded bits consists of \(m\)\((m\ >1)\) bits shortened information and \(k-m\) bits information. The codeword of shortened code is obtained by removing \(m\) bits shortened information from the codeword of \((n,k)\) code. \((n-m,k-m)\) shortened code uses only a limited number of codewords in \((n,k)\) code, and the minimum distance of \((n-m,k-m)\) shortened code is not smaller than the minimum distance of \((n,k)\) code. \begin{table}
\begin{tabular}{c c} \hline \hline
**Term/Symbol** & **Definition** \\ \hline Shortened information & Information to be removed after encoding \\ Unencoded bits & Bit sequence containing the shortened information and information \\ Column weight & Number of 1’s in column of information bits of the parity check matrix \\ Row weight & Number of 1’s in row of information bits of the parity check matrix \\ \(k\) & Unencoded bit length \\ \(n\) & Codeword length \\ \(m\) & Shortened information length \\ \(t\) & Number of bits that can be decoded by decoder of \((n,k)\) code \\ \(s\) & Number of bits that can be decoded by decoder of \((n-m,k-m)\) \\  & shortened code without the shortened information \\ \(E\) & Efficiency of \((n,k)\) code \\ \(E_{y}\) & Efficiency of \((n-m,k-m)\) shortened code \\  & when decoder uses the shortened information \\  & Efficiency of \((n-m,k-m)\) shortened code \\ \(E_{z}\) & when decoder does not use the shortened information \\ \(q\) & Column weight \\ \(r\) & Row weight \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definitions of terms and symbols. Figure 1: Proposed dependable wireless system. Integrated terminal uses multiple radio access technologies (RATs) such as cellular, ultra-wide band (UWB), Bluetooth, and wireless local area network (LAN) to communicate simultaneously. If \((n,k)\) code can correct \(t\) bit errors, the efficiency is defined as \(E\). \[E=\frac{t}{n} \tag{1}\]  
\((n-m,k-m)\) shortened code can correct \(t\) bit errors, if the decoder uses the shortened information. The efficiency \(E_{y}\) is expressed by the following equation. \[E_{y}=\frac{t}{n-m} \tag{2}\]  
From Equations (1) and (2), the relationship between \(E\) and \(E_{y}\) is as follows. \[E<E_{y} \tag{3}\]  
This indicates that the error correction capability is improved by shortening, and the same error rate can be obtained at a lower SNR than before shortening under an additive white Gaussian noise (AWGN) channel. If the decoder does not use the shortened information, only \(s\) (\(s\leq t\)) bit errors can be corrected by the decoder. The efficiency \(E_{z}\) is expressed by the following equation. \[E_{z}=\frac{s}{n-m} \tag{4}\]  
Since the decoder does not use the shortened information, it is easy to imagine that \(s\) decreases rapidly as \(m\) increases. The relation between \(E_{z}\) and \(E\) is as follows. \[E_{z}\leq E \tag{5}\]  
If the sender and the receiver share the shortened information, and the sender and the cyberterrorist do not share the shortened information, by changing the shortened information length, it is possible to provide a gap in the required SNR for the receiver and the cyberterrorist. To realize this, the shortened information must be shared securely between the sender and the receiver. Then, countermeasures against wiretapping and attacks can be realized simultaneously. We adopted shortened repeat-accumulate (RA) code as the shortened code from the viewpoint that the construction of the encoder is simple, but it is also applicable to the Turbo code, low-density parity check (LDPC) code, and Polar code used in 5G. RA code is a code which was proposed in 1998 by [PERSON] et al. [26]. Figure 3 shows the structure of systematic RA code encoder.