# Blind Interleaver Parameters Estimation Using Kolmogorov-Smirnov Test
## 5 Discussion and Conclusions  
In this paper, we proposed a blind interleaver parameters estimation algorithm based on a combination of the K-S test and multinomial distribution in noisy channels. To compare the performance from various perspectives, we compared the false alarm rates according to the length of the available bitstream, the detection probability according to code rates, and execution time. The performance of the proposed estimation algorithm was superior to that of Bernoulli, KLD, Multinomial, and MDS.  
We exploited the fact that rank distributions of linear codes differ significantly from those of random sequences owing to the linear dependence of linear codes. To estimate interleaver periods using that property, we adopted the K-S test as a measure of the probability matching problem between the two rank distributions of the random binary signal and the received signal. After finding the final candidate of the interleaver period, we adopted Multinomial [6] to control false alarm rates. The value of (1) is lower than a threshold, it is enough to judge that it does not happen by chance.  
In terms of probability matching metric, KLD includes logarithmic operations and considers all values between two PDFs, but the our method does not involve logarithmic calculations and finds the largest difference between the two CDFs. Despite the absence of logarithmic operations, our approach took 0.14 s longer than KLD, but with shorter execution times than Multinomial and MDS.  
Through the experimental results, the proposed algorithm is verified by comparing false alarm rates, the estimated performance, and execution time. In terms of false alarm rates, the probability of false alarm appears as low as KLD. We can see that our algorithm outperforms Bernoulli, KLD, Multinomial, and MDS in terms of detection probability. Also, we calculate execution time for Bernoulli, KLD, Multinomial, MDS, and our method. Although our method was the third fastest among the compared algorithm, we can see that the computational complexity of the proposed method was about 48% lower than that of MDS. Experimental results verified that our method outperformed the previous algorithms with a relatively low computational complexity.  
Conceptualization, S.W. and C.C.; methodology, S.W. and C.C.; software, S.W.; validation, S.W. and C.C.; writing--review and editing, S.W.; project administration, J.J. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations and symbols are used in this manuscript:  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & \(t\) **(s)** \\ \hline Bernoulli [4] & 11.5610 \\ KLD [5] & 11.4486 \\ Multinomial [6] & 14.3958 \\ MDS [9] & 22.3636 \\ Proposed & 11.5862 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the average run times when \(S=30\) with BCH (15, 11) code.