A Universe Digital Data Scrambler

A Universal Digital Data Scrambler By DAVID G. L E E P E R (Manuscript received May 22, 1973) Analyses in the literature of digital communications often presuppose that the digital source is "ivhite," that is, that it produces stochastically independent equiprobable symbols. In this paper we show that it is possible to "whiten" to any degree all the first- and second-order statistics of any binary source at the cost of an arbitrarily small controllable error rate. Specifically, we prove that the self-synchronizing digital data scrambler, already shown effective at scrambling strictly periodic data sources, will scramble any binary source to an arbitrarily small first- and secoiid-order probability density imbalance 8 if (i) the source is first passed through the equivalent of a symmetric memoryless channel with an arbitrarily small but nonzero error probability e, and (ii) the scrambler contains M stages where M ^ 1 + log 2 [(ln 25)/In (1 - 2c)]. Some interpretations and applications of this result are included.