### Abstract

We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R_{2} based both on Y and n the message it received about X. The decoder's task is to estimate a function of X and Y. For example, we consider the minimum mean squared-error distortion when encoding the sum of jointly Gaussian random variables under these constraints. We also characterize the rates needed to reconstruct a function of X and Y losslessly. Our general contribution toward understanding the limits of the cascade multiterminal source coding network is in the form of inner and outer bounds on the achievable rate region for satisfying a distortion constraint for an arbitrary distortion function d(x, y, z). The inner bound makes use of a balance between two encoding tactics-relaying the information about X and recompressing the information about X jointly with Y. In the Gaussian case, a threshold is discovered for identifying which of the two extreme strategies optimizes the inner bound. Relaying outperforms recompressing the sum at the relay for some rate pairs if the variance of X is greater than the variance of Y.

Original language | English (US) |
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Title of host publication | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |

Pages | 1199-1203 |

Number of pages | 5 |

DOIs | |

State | Published - 2009 |

Event | 2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: Jun 28 2009 → Jul 3 2009 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8102 |

### Other

Other | 2009 IEEE International Symposium on Information Theory, ISIT 2009 |
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Country | Korea, Republic of |

City | Seoul |

Period | 6/28/09 → 7/3/09 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*2009 IEEE International Symposium on Information Theory, ISIT 2009*(pp. 1199-1203). [5205989] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2009.5205989