A Coder-Decoder model for use in Lossless Data Compression

This article describes a technique of using a trigonometric function and combinatorial calculations to code or transform any finite sequence of binary numbers (0s and 1s) of any length to a unique set of three Real numbers. In reverse, these three Real numbers can be used independently to reconstruct the original Binary sequence precisely. The main principles of this technique are then applied in a proposal for a highly efficient model for Lossless Data Compression. The core of this technique makes use of the observation that vertical projections of successive circular sector chords can form a sequence of values that are of unique properties and can be mapped exactly to any Binary sequence. The purpose of this technique is to utilize these properties in order to devise a Coder-Decoder Transform and a potential Data Compression algorithm. In particular, we will deduce an ordinary Trigonometric function to map a quadrant of a circle to a given Binary sequence of finite length and yield three Real numbers that are unique and can be derived directly from the original sequence of Binary numbers. These unique three Real numbers can be then used independently to reconstruct the original Binary sequence precisely. To illustrate how to arrive at this Trigonometric function, consider a circle of radius r having its first quadrant divided into N equal circular sectors. The above diagram depicts one such generic circular sector for the purpose of visualizing this technique. It follows that the central angle, θ, for each generic sector is θ = π/2N