The Lossless Adaptive Binomial Data Compression Method

Abstract

In this paper, we propose a new method for the binomial adaptive compression of binary sequences of finite length without loss of information. The advantage of the proposed binomial adaptive compression method compared with the binomial compression method previously developed by the authors is an increase in the compression rate. This speed is accompanied in the method by the appearance of a new quality—noise immunity of compression. The novelty of the proposed method, which makes it possible to achieve these positive results, is manifested in the adaptation of the compression ratio of compressible sequences to the required time, which is carried out by dividing the initial set of binary sequences into compressible and incompressible sequences. The method is based on the theorem proved by the authors on the decomposition of a stationary Bernoulli source of information into the combinatorial and probabilistic source. The last of them is the source of the number of units. It acquires an entropy close to zero and practically does not affect the compression ratio at considerable lengths of binary sequences. Therefore, for the proposed compression method, a combinatorial source generating equiprobable sequences is paramount since it does not require a set of statistical data and is implemented by numerical coding methods. As one of these methods, we choose a technique that uses binomial numbers based on the developed binomial number system. The corresponding compression procedure consists of three steps. The first is the transformation of the compressible sequence into an equilibrium combination, the second is its transformation into a binomial number, and the third is the transformation of a binomial number into a binary number. The restoration of the compressed sequence occurs in reverse order. In terms of the degree of compression and universalization, the method is similar to statistical methods of compression. The proposed method is convenient for hardware implementation using noise-immune binomial circuits. It also enables a potential opportunity to build effective systems for protecting information from unauthorized access.