## Abstract

The Blackwell-Le Cam decision theory provides an approximation framework for statistical experiments in terms of expected risks of optimal decision procedures. The Blackwell partial order formalizes an intuitive notion of which experiment of a given pair is "more informative" for the purposes of inference. The Le Cam deficiency is an approximation measure for any two statistical experiments (with the same parameter space), and it tells us how much we will lose if we base our decisions on one experiment rather than another. In this paper, we develop an extension of the Blackwell-Le Cam theory, starting from a partial ordering for channels introduced by Shannon. In particular, we define a new approximation measure for channels, which we call the Shannon deficiency, and use it to prove an approximation theorem for channel codes that extends an earlier result of Shannon. We also construct a broad class of deficiency-like measures for channels based on generalized divergences, relate them to several alternative notions of capacity, and prove new upper and lower bounds on the Le Cam deficiency.

Original language | English (US) |
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Title of host publication | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |

Pages | 1220-1224 |

Number of pages | 5 |

DOIs | |

State | Published - 2011 |

Externally published | Yes |

Event | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: Jul 31 2011 → Aug 5 2011 |

### Other

Other | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 7/31/11 → 8/5/11 |

## ASJC Scopus subject areas

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