# Source Symbol Purging-Based Distributed Conditional Arithmetic Coding
## 4 Simulation Results  
This section presents simulation results to evaluate the performance of the proposed scheme. Since the SPDCAC encoder encodes the source sequence \(X\) with a code rate less than \(H(X)\), the SPDCAC decoder cannot directly decode the received codeword to restore \(X\). Therefore, we investigate the encoding performance of SPDCAC and the minimum code rate required of SPDCAC to achieve lossless decoding with the help of a side information sequence that has a strong correlation with \(X\). As the correlation strength between the source sequence and the side information sequence gradually weakens, errors in the decoded results are also gradually increasing. The decoding performance of SPDAC with the assistance of different side information is also our focus. Since the scheme proposed in this article needs to use the context model in the coding process, a randomly generated binary order-1 Markov source sequence of length \(N\) will be used as the source sequence \(X\). The transition probability matrix of the Markov source is shown in Table 1, where the value of \(P_{t}\) is positively correlated with the strength of the correlation between adjacent symbols in the source sequence. All schemes based on arithmetic coding in subsequent experiments will use the order-1 context model in the coding process.  
The code rate unit of all DSC schemes is bit/symbol (\(b/s\)), which is obtained by dividing the number of bits of the codeword output from the encoder by the number of source symbols. The side information sequence \(Y\) is generated by sending the source sequence \(X\) through a virtual BSC. Every symbol in \(Y\) is transmitted to the decoder losslessly. The correlation between \(X\) and \(Y\) is controlled by the transition probability of BSC (the transition probability of BSC is \(p_{c}\)), and the conditional entropy \(H(X|Y)\) between \(X\) and \(Y\) is used to represent the correlation between them. \(H(X|Y)=H(p_{c})=-p_{c}log_{2}p_{c}-(1-p_{c})log_{2}(1-p_{c})\)[24]. A smaller \(H(X|Y)\) means there is a higher similarity between \(X\) and \(Y\). The conditional entropy \(H(X|Y)\) was set to \(0.1\sim 0.5\) in experiments. Many DSC studies use BER as the performance evaluation index of decoding, which is used to indicate the ratio of the number of error bits to the total number of bits in the decoding result. It is also used to show the decoding performance in our experiments. In our experiment, the purging rates of the encoder and the decoder were preset to be the same. The interval expansion factor \(\alpha\) of the DSC scheme based on expanding probability intervals was also preset to be the same in the encoder and the decoder. Due to the randomness of the generated source sequence, each result shown in the following figures and tables is the averaged value of \(10^{3}\) experiments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Transition Probability** & \(X_{i}=0\) & \(X_{i}=1\) \\ \hline \(X_{i-1}=0\) & \(P_{t}\) & \(1-P_{t}\) \\ \hline \(X_{i-1}=1\) & \(1-P_{t}\) & \(P_{t}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Transition probability matrix.