### Abstract

The problem of estimating an arbitrary random variable from its observation corrupted by additive white Gaussian noise, where the cost function is taken to be the minimum mean p-th error (MMPE), is considered. The classical minimum mean square error (MMSE) is a special case of the MMPE. Several bounds and properties of the MMPE are derived and discussed. As applications of the new MMPE bounds, this paper presents: (a) a new upper bound for the MMSE that complements the 'single-crossing point property' for all SNR values below a certain value at which the MMSE is known, (b) an improved characterization of the phase-transition phenomenon which manifests, in the limit as the length of the capacity achieving code goes to infinity, as a discontinuity of the MMSE, and (c) new bounds on the second derivative of mutual information, or the first derivative of MMSE, that tighten previously known bounds.

Original language | English (US) |
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Title of host publication | Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1646-1650 |

Number of pages | 5 |

ISBN (Electronic) | 9781509018062 |

DOIs | |

State | Published - Aug 10 2016 |

Externally published | Yes |

Event | 2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: Jul 10 2016 → Jul 15 2016 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2016-August |

ISSN (Print) | 2157-8095 |

### Other

Other | 2016 IEEE International Symposium on Information Theory, ISIT 2016 |
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Country | Spain |

City | Barcelona |

Period | 7/10/16 → 7/15/16 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory*(pp. 1646-1650). [7541578] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541578