### Abstract

The indirect source-coding problem in which a Bernoulli process is compressed in a lossy manner from its noisy observations is considered. These noisy observations are obtained by passing the source sequence through a binary symmetric channel so that the channel crossover probability controls the amount of information available about the source realization at the encoder. We use classic results in rate-distortion theory to compute the rate-distortion function for this model as a solution of an exponential equation. In addition, we derive an upper bound on the rate distortion which has a simple closed-form expression and investigate the coding scheme that attains it. These expressions capture precisely the expected behavior of the rate-distortion function: the noisier the source observations, the smaller the reduction in distortion obtained from increasing the compression rate.

Original language | English |
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Title of host publication | ITW 2015 - 2015 IEEE Information Theory Workshop |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 352-356 |

Number of pages | 5 |

ISBN (Electronic) | 9781467378529 |

DOIs | |

State | Published - 17 Dec 2015 |

Event | IEEE Information Theory Workshop, ITW 2015 - Jeju Island, Korea, Republic of Duration: 11 Oct 2015 → 15 Oct 2015 |

### Publication series

Name | ITW 2015 - 2015 IEEE Information Theory Workshop |
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### Conference

Conference | IEEE Information Theory Workshop, ITW 2015 |
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Country | Korea, Republic of |

City | Jeju Island |

Period | 11/10/15 → 15/10/15 |

### Keywords

- Binary source
- Binary symmetric channel
- Indirect rate distortion

## Cite this

*ITW 2015 - 2015 IEEE Information Theory Workshop*(pp. 352-356). [7360794] (ITW 2015 - 2015 IEEE Information Theory Workshop). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ITWF.2015.7360794