Polynomial Representation of Binary Trees of Entropy Binary Codes

Abstract

An important component of streaming large amounts of information are algorithms for compressing information flow. Which in turn are divided into lossless compression algorithms (entropic) - Shannon, Huffman, arithmetic coding, conditional compression - LZW, and otherinformation cone injections and lossy compression algorithms - such as mp3, jpeg and others. It is important to follow a formal strategy when building a lossy compression algorithm. It can be formulated as follows. After describing the set of objects that are atomic elements of exchange in the information flow, it is necessary to build an abstract scheme of this description, which will determine the boundary for abstract sections of this scheme, which begins the allowable losses. Approaches to the detection of an abstract scheme that generates compression algorithms with allowable losses can be obtained from the context of the subject area. For example, an audio stream compression algorithm can divide a signal into simple harmonics and leave among them those that are within a certain range of perception. Thus, the output signal is a certain abstraction of the input, which contains important information in accordance with the context of auditory perception of the audio stream and is represented by less information. A similar approach is used in the mp3 format, which is a compressed representation. Unlike lossy compression algorithms, entropic compression algorithms do not require contextanalysis, but can be built according to the frequency picture. Among the known algorithms for constructing such codes are the Shannon-Fano algorithm, the Huffman algorithm and arithmetic coding. Finding the information entropy for a given Shannon code is a trivial task. The inverse problem, namely finding the appropriate Shannon codes that have a predetermined entropy and with probabilities that are negative integer powers of two, is quite complex. It can be solved by direct search, but a significant disadvantage of this approach is its computational complexity. This article offers an alternative technique for finding such codes.