Abstract
We address the problem of improving the performance of asymmetric M-PAM signal constellations in Euclidean space by embedding them in hyperbolic space when the communications system designer is bounded to using this modulation. We derive the probability density function of the additive noise in one dimensional hyperbolic space by showing that it is a log-normal random variable. From this, we determine the optimum receiver for the M-PAM signal constellations in one dimensional hyperbolic space, and show that it is equivalent to the optimum receiver in the Euclidean space. Finally, we compare the performance of the communication system using M-PAM signal constellations in one dimensional hyperbolic space with the corresponding system in the Euclidean space. We show that the symmetric M-PAM signal constellations in one dimensional hyperbolic space derived from the corresponding asymmetric M-PAM in the Euclidean space have asymptotic coding gains.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
