On the issue of modeling long biometric codes with dependent bit states

The article considers a problem of modeling long output codes for the neural network transformer of analogue (continuous) biometric data into the output digital code. Modeling of independent code strings is not a complicated problem. For example, in order to model a single 256-bit code it is sufficient to execute a 256-fold reference to the software or hardware random-number generator. After that, one may find a matrix of biometric code bits correlations and build a proper matrix of transformation for it. It is technically feasible to calculate thecorrelation matrix and the corresponding matrix transformation for codes of 2-16 bits length. However, this method works out only for the codes of short length. Beyond this limit the problem becomes incorrect. Thereby, it is necessary to synthesize the matrix binding independent data by means of another non-classical algorithm. The new concept of binding independent pseudorandom data is based on the necessity to synthesize a certain data-binding matrix which would save only statistics of correlations. If the precise transformation is impossible to create, the transformation providing the required pair correlation coefficient distribution is real. As a result of statistical investigation the authors have built a nomogram of connection between the controlled modeling parameters and the mathematical expectation of the module of pair cor- relation coefficients with the length of parameters' vector n = 2, 4, 8, 16, 32, 64, 128. Nomogram results show that the increase of problem's dimensionality causes the values of pair correlation coefficients r(a) to tend closer and closer to the coordinate axes. In general, evaluation of r(a) function is quite a simple problem not requiring any considerable computing resources. The controlled parameter "a" is conveniently located in the range from 0.0 to 1.0, as well as the module of pair correlation coefficients. Thus, one may obtain the distribution of biometric data (biometric codes) generator with the possibility to control the mathematical expectation and the root-mean-square deviation of distribution of pair correlation coefficients of biometric data and biometric codes.