# Blind Interleaver Parameters Estimation Using Kolmogorov-Smirnov Test
## 4 Results  
In this section, we present experimental results and compare the performance of the proposed algorithm to that of previous algorithms. To generate bitstreams, a (7, 4) binary Hamming code and two BCH codes, (15, 5), (15, 7), and (15, 11) were used [1]. The generated bit length was 50,000 and a random block interleaver was used. Instead of the signal-to-noise ratio(SNR), we compare the performance of each algorithm based on the probability of errors occurring in the channel. We assumed that the interleaved bitstream passed through a binary symmetric channel with different bit error rates (BER), and even considered the possibility that the data collected by the receiver would have been translated. The number of trials for constructing rank distributions was 500 for each searching process. For each BER, we tested the process for calculating the probability of estimating interleaver parameters 1000 times. Given the interleaver period, \(S\), the search range of the predicted interleaver period, \(l\), was set from 7 to \(S+1\). The search range of the randomly chosen translation value, \(d\), was set from 0 to \(l-1\). We compared the performance of the proposed algorithm with that of algorithms based on Bernoulli trials [4], KLD [5], Multinomial [6], and MDS [9]. In the case of Bernoulli [4], the interleaver period was predicted when the number of success events is maximum. In KLD [5], the interleaver period is predicted when (2) is maximum. Likewise, Multinomial [6] predicts interleaver periods by finding the minimum value of (1), and MDS finds the predicted length \(l\) with the maximum value of (3). To show objective performance comparison, we denote detection probability as below:  
\[P_{D}=\frac{C_{N}}{E_{N}} \tag{6}\]  
where \(E_{N}\) is the total number of times the interleaver period is estimated, and \(C_{N}\) is the number of times among \(E_{N}\) predicted correctly. Figures 5-7 show the experimental results in terms of code rates, interleaver periods, and the lengths of the intercepted bitstream, respectively. Since the value of (5) varies depending on the linearity of the codewords in the received data, so the higher the probability that the linearity of the codeword is not maintained, the faster the performance deteriorates according to the increase of BER. To compare performances based on the code rates, two BCH codes were used with 50,000 intercepted symbols. As shown in Figure 5, we can see that the proposed algorithm had the highest detection probability of blind estimating interleaver parameters regardless of the code rate change. It can be seen that when the code rate is high, performance degradation begins at the lower BER than when the code rate is low. Further, Figure 5a,b show that the higher the code rates, the lower the detection probability for the same BER. In terms of interleaver periods, we compared the performances of the proposed algorithm with the previous algorithms. Two interleaver periods, 28 and 42, were used and bitstreams of length 50,000 were generated using Hamming (7, 4) code. Figure 6 shows that the performance of our algorithm is better than that of other algorithms in both interleaver periods. From Figure 5(a),b, we observe that the performance deteriorated when the interleaver periods increased because the probability that the constructed matrices for rank calculation contain errors increases. When comparing the performances based on the lengths of the intercepted bitstreams, we ran the test 10,000 times for each BER to achieve more accurate results. Figure 7 visualizes the detection and false alarm probability when the lengths of the bitstreams are 50,000 and 5000. When the BER is lower than 0.04, we can see that the longer the length of the intercepted bitstreams, the higher is the performance for each method. However, when the BER is higher than 0.04, we observed that the performance with shorter intercepted symbols was the better in terms of detection probability. Further, the proposed algorithm had the lowest false alarm rates as shown in Figure 6(b).