### Abstract

Communication of quantized information is frequently followed by a computation. We consider situations of distributed functional scalar quantization: distributed scalar quantization of (possibly correlated) sources followed by centralized computation of a function. Under smoothness conditions on the sources and function, companding scalar quantizer designs are developed to minimize mean-squared error (MSE) of the computed function as the quantizer resolution is allowed to grow. Striking improvements over quantizers designed without consideration of the function are possible and are larger in the entropy-constrained setting than in the fixed-rate setting. As extensions to the basic analysis, we characterize a large class of functions for which regular quantization suffices, consider certain functions for which asymptotic optimality is achieved without arbitrarily fine quantization, and allow limited collaboration between source encoders. In the entropy-constrained setting, a single bit per sample communicated between encoders can have an arbitrarily large effect on functional distortion. In contrast, such communication has very little effect in the fixed-rate setting.

Original language | English (US) |
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Article number | 5961835 |

Pages (from-to) | 5298-5325 |

Number of pages | 28 |

Journal | IEEE Transactions on Information Theory |

Volume | 57 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2011 |

Externally published | Yes |

### Keywords

- Asymptotic quantization theory
- distributed source coding
- optimal point density function
- rate-distortion theory

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*57*(8), 5298-5325. [5961835]. https://doi.org/10.1109/TIT.2011.2158882