A modified hyperbolic congruential frequency hop codes for asynchronous event signaling

We show that the modified hyperbolic congruential frequency hop codes have almost ideal properties for code division multiple access (CDMA) communications, that is, for any pair of the codewords they have at most two hits for any frequency shift under a synchronous environment and at most four hits for any time and frequency shift under an asynchronous environment. Efficient algorithms for decoding the proposed codes are presented subsequently. We further demonstrate the applicability of the codes by showing a one way asynchronous CDMA communication system over power distribution line networks