Pseudonoise with Arbitrary Amplitude Distribution--Part I: Theory

Abstract

Many cases arise in practice where a versatile hardwired pseudorandom number or pseudonoise generator would be extremely useful. General-purpose pseudonoise devices are not available today. We present a new sampling method, conditional bit sampling, which is suited for hardwired sampling devices because of its generality, simplicity, and accuracy. Random variables sampled from an arbitrary distribution are generated bit by bit from high- to low-order bits with the conditional bit algorithm. The result of a comparison of a uniform number to a conditional probability determines whether a bit in the sampled random number is set to one. The conditional probabilities are easily calculated for any probability distribution and must be arranged in special order. Simple Fortran programs make all necessary computations. Agreement between actual and theoretical performance of the conditional bit algorithm was excellent when sampling accuracy was evaluated for several examples of continuous and discrete densities. Sampling from empirically known, perhaps erratic-shaped, densities presents no problems. Only a small memory containing the conditional probabilities needs to be changed to alter the sampled distribution. The conditional bit algorithmic process always remains the same.