Second-Order Spline-Wavelet Robust Code under Non-Uniform Codeword Distribution.

In computer science, robustness is the ability of a computer system to cope with errors during execution. Robust codes are new nonlinear systematic error detecting codes that provide uniform protection against all errors, whereas classical linear error detection code detects only a certain class of errors. Therefore, defence by the linear codes can be ineffective in many channels and environments, when error distribution is unknown. The probability of error masking can increase depending on codeword distribution. However, mapping the most probable codewords to a predefined set can reduce the maximum of the error masking distribution. The algorithm proposed in this paper is based on the second-order wavelet decomposition of B-splines under non-uniform nets. In this paper, we propose a general approach to the algorithm construction of spline-wavelet decompositions of linear space over an arbitrary field. This approach is based on the generalization of calibration relations and functional systems, which are biorthogonal to basic systems of relevant space. The obtained results permit the construction of second-order spline-wavelet robust code. [ABSTRACT FROM AUTHOR]