DMCA
Applications of Pseudorandom Binary Sequences Generated by One-dimensional Discrete-time Maps
BibTeX
@MISC{Djonin_applicationsof,
author = {Dejan Djonin},
title = {Applications of Pseudorandom Binary Sequences Generated by One-dimensional Discrete-time Maps},
year = {}
}
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Abstract
Abstract: Inspired by recently reported applications of chaotic dynamical systems in encryption and asynchronous DS-CDMA systems [1], as well as our prior study of properties of non-linear maps [2], we present two new improved methods for generation of error-correction codes by iteration of one-dimensional non-linear discrete-time maps. In this correspondence we focus our attention on the particular class of discrete-time maps whose dynamics is governed by the m-adic shift defined on unit interval as Sm(x)=mxmod1, for m = 2,3,4, … which presents a generalization of well known Bernoulli shift. m-adic shift can produce ergodic sequences for almost all initial conditions on unit interval. It can be shown that invariant measure is uniform for m-adic shift. Furthermore, it can be shown that it is possible to create a sequence of independent identically distributed (i.i.d.) binary random numbers by discrete-valued observation function of real sequences generated by these maps for arbitrary choice of initial condition drawn from the unit interval. General conditions needed for a non-linear function and discrete-valued observation function to produce a sequence of i.i.d. random binary numbers are also discussed. Suggested error-correction codes are based on this result and present efficient deterministic construction of block codes that have favorable properties common to the random codes. Both methods can be equally applied on construction of binary and codes whose code signs have continuos amplitude.
Keyphrases
unit interval m-adic shift pseudorandom binary sequence one-dimensional discrete-time map error-correction code discrete-valued observation function block code particular class code sign real sequence non-linear map random code favorable property discrete-time map arbitrary choice prior study ergodic sequence bernoulli shift non-linear function one-dimensional non-linear discrete-time map invariant measure initial condition random binary number present efficient deterministic construction initial condition drawn chaotic dynamical system general condition binary random number asynchronous ds-cdma system
