Bit Error Probability and Bit Outage Rate in Chaos Communication

Abstract

This paper investigates the notion of the probability of bit error (PBE) and its distribution in chaos-based communication systems; these are seen as being the fundamental quantities to both the well-known bit error rate (BER) and the new concept in chaos communications of bit outage rate (BOR). The form of the distribution illustrates the degree to which bit error rate is a stable representation of performance. Bit outage rate is another measure of performance which gives practically helpful information about bit error. For a simple coherent chaos-shift-keying system the distribution of bit error probability is derived exactly, and theoretically exact formulas for the bit outage rate and bit error rate are presented. Two specific cases are developed to obtain useful qualitative and quantitative information. The cases concern independent Gaussian spreading, as a lower benchmark and logistic map spreading, as typical of effective chaotic spreading. Comparisons are obtained between these spreading distributions and between different extents of their spreading, calibrated against per bit signal to noise ratio. A general conclusion is that bit outage and bit error rates are complementary measures of performance.