Algorithms of constructing linear and robust codes based on wavelet decomposition and its application

Abstract

This article presents the algorithms of constructing error detecting codes using wavelet decomposition. Linear code, presented in the paper, based on the coefficients of scaling function of wavelet transformation. Constructed linear code was used for creation of robust codes that have a smaller number of undetectable errors and have an ability to detect any error with a predetermined probability. Robust codes are generated by applying a nonlinear function to the redundancy part of the linear code. The article describes comparative characteristics between the proposed wavelet code constructions and other error detecting codes. The paper proposes two constructions of robust code, first robust code base on the multiplicative inverse in a finite field, redundancy part of second code construction build as a cube in the field of the information component. The paper describes a model of application proposed code constructions in ADV612 system. Characteristics of robustness of the described model for uniform and nonuniform codeword distribution are also presented in the paper.