Codes for spread spectrum applications generated using chaotic dynamical systems

An approach to finding codes for use in direct sequence spread spectrum com munications systems is described. It is based upon an analogy between codes having auto- and cross-correlation properties desirable for spread spectru m systems, and certain dynamical systems encountered in ergodic theory call ed systems with 'Lebesgue spectrum'. Such systems are associated with colle ctions of orthogonal functions and these functions can be used to generate collections of time series with zero cross-correlation functions. To genera te codewords we must use truncated versions of these time series, for which the cross-correlations are no longer precisely zero: these truncated seque nces correspond to periodic orbits of the dynamical system. The method for finding a code from a suitable periodic orbit is described, and an example, using a simple dynamical system known as the doubling map, is worked throu gh in some detail.