## 2 General Analysis of the Binomial Adaptive Compression Method
### Analysis of the Proposed Compression Method  
The considered compression method belongs to the class of numbering compression methods and does not require preliminary statistical tests, which is its advantage. Compared with other numbering compression methods, it is versatile and dynamic, expressed in adaptation to the source of information, reducing the compression time. As a result, the compression ratio increases, and the cost of the equipment implementing the method becomes cheaper. In addition, the method allows for detecting errors, thereby improving the noise immunity of compression. The method also includes the ability to protect information from unauthorized access. The compression methods proposed above in the introduction, which have a high compression ratio and speed, are primarily specialized. Universal methods, especially those requiring statistical studies, are less fast. At the same time, both methods, during compression, reduce the noise immunity of the compressed information by eliminating redundancy. It is possible to eliminate the shortcomings of existing compression methods by solving the task of the optimal adaptive control of the values of their compression ratios, noise immunity, and compression time. The proposed adaptive method is based on the method developed for the universal compression of binary sequences based on binomial numbers. The universality of the proposed method of adaptive binomial compression is explained by the fact that it compresses binary sequences. Moving from binary sequences to processing symbolic, graphic, and more complex information is relatively easy. In addition, many messages and images themselves are represented as binary sequences. These include television binary images, graphics, and symbols. However, the binomial compression method compressed all binary sequences without exception, significantly increasing the compression time since many of the binary sequences gave almost zero compression ratio or even negative. In this paper, we propose to solve this task using adaptive selective compression of binary sequences, in which inefficient sequences are not compressed. Accordingly, the task of this paper is to develop a universal binomial information compression method that does not require preliminary statistical tests, adaptively optimally regulating the value of the compression ratio, time, and noise immunity. This paper is research; therefore, it does not provide information on the practical application of results. The reliability of the obtained scientific results was verified experimentally on computer models and in separate works on the theoretical study of the method. It is easy to check it for specific examples in manual mode without additional calculations by the method proposed in the paper. Practical applications of the proposed adaptive binomial compression method are most effective in mobile communication systems operating under interference. This method also can compress texts, graphics, and images. In this case, the longer the compressed binary block, the more efficient the compression. This method can be especially effective in hardware implementation. In terms of speed, compression ratio, and noise immunity, the method, under certain conditions, can significantly surpass the known compression methods. The peculiarity of the method is its adaptability, which means obtaining maximum efficiency under the conditions of changing probabilities of generated binary sequences. It can give a gain in performance and a loss in the compression ratio and vice versa, giving the most significant overall effect. Therefore, its comparison with conventional compression methods is not correct. To date, adaptive binomial methods in compression systems were first proposed by the authors. The disadvantage of the method is the complexity of implementation and lack of universality. Changing the probabilities requires changing the adaptive properties of the method, which complicates its structure.