## Abstract

We consider a two-terminal variant (double-sided) of the information bottleneck problem, which is related to biclus-tering. In our setup, x and Y are dependent random variables and the problem is to find two independent channels \mathrm{P}_{\cup 1\times} and \mathrm{p}_{\vee 1!} (setting the Markovian structure \cup\rightarrow\times\rightarrow \mathrm{Y}\rightarrow V) that maximize I(\cup;\mathrm{V}) subject to constraints on the relevant mutual information expressions: I(\cup;\mathrm{X}) and I(\mathrm{V};\mathrm{Y}). For jointly Gaussian X and Y, we show that Gaussian channels are optimal in the low-SNR regime, but not for general SNR. Similarly, it is shown that for a doubly symmetric binary source, binary symmetric channels are optimal when the correlation is low, and are suboptimal for high correlation. We conjecture that Z and S channels are optimal when the correlation is 1 (i.e., \mathrm{X}=\mathrm{Y}), and provide supporting numerical evidence.

Original language | American English |
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Title of host publication | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2495-2500 |

Number of pages | 6 |

ISBN (Electronic) | 9781538682098 |

DOIs | |

State | Published - 12 Jul 2021 |

Event | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2021-July |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2021 IEEE International Symposium on Information Theory, ISIT 2021 |
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Country/Territory | Australia |

City | Virtual, Melbourne |

Period | 12/07/21 → 20/07/21 |

### Bibliographical note

Funding Information:The work has been supported by the European Union’s Horizon 2020 Research And Innovation Programme, grant

Funding Information:

agreement no. 694630, by the ISF under Grant 1791/17, and by the WIN consortium via the Israel minister of economy and science.

Publisher Copyright:

© 2021 IEEE.