An Upper Bound for Signal Transmission Error Probability in Hyperbolic Spaces

TL;DR

This paper introduces a Gaussian probability density function for hyperbolic spaces and establishes an upper bound for signal transmission error probability based on hyperbolic distance, aiding in coding and decoding analysis.

Contribution

It develops a Gaussian pdf for hyperbolic spaces and derives an upper bound for error probability, advancing signal processing in hyperbolic geometry.

Findings

Gaussian pdf for hyperbolic space introduced

Upper bound for error probability established

Analysis based on Poincare models

Abstract

We introduce and discuss the concept of Gaussian probability density function (pdf) for the n-dimensional hyperbolic space which has been proposed as an environment for coding and decoding signals. An upper bound for the error probability of signal transmission associated with the hyperbolic distance is established. The pdf and the upper bound were developed using Poincare models for the hyperbolic spaces.