### Abstract

This paper studies an n-dimensional additive Gaussian noise channel with a peak-power-constrained input. It is well known that, in this case, the capacity-achieving input distribution is supported on finitely many concentric shells. However, due to the previous proof technique, neither the exact number of shells of the optimal input distribution nor a bound on it was available.This paper provides an alternative proof of the finiteness of the number shells of the capacity-achieving input distribution and produces the first firm upper bound on the number of shells, paving an alternative way for approaching many such problems. In particular, for every dimension n, it is shown that the number of shells is given by O(A^{2}) where A is the constraint on the input amplitude. Moreover, this paper also provides bounds on the number of points for the case of n = 1 with an additional power constraint.

Original language | English (US) |
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Title of host publication | 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1907-1911 |

Number of pages | 5 |

ISBN (Electronic) | 9781538692912 |

DOIs | |

State | Published - Jul 2019 |

Event | 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: Jul 7 2019 → Jul 12 2019 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2019-July |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2019 IEEE International Symposium on Information Theory, ISIT 2019 |
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Country | France |

City | Paris |

Period | 7/7/19 → 7/12/19 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings*(pp. 1907-1911). [8849318] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849318