### 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) |
---|---|

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 |

### Fingerprint

### 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

### Cite this

*IEEE Transactions on Information Theory*,

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

**Distributed scalar quantization for computing : High-resolution analysis and extensions.** / Misra, Vinith; Goyal, Vivek K.; Varshney, Lav R.

Research output: Contribution to journal › Review article

*IEEE Transactions on Information Theory*, vol. 57, no. 8, 5961835, pp. 5298-5325. https://doi.org/10.1109/TIT.2011.2158882

}

TY - JOUR

T1 - Distributed scalar quantization for computing

T2 - High-resolution analysis and extensions

AU - Misra, Vinith

AU - Goyal, Vivek K.

AU - Varshney, Lav R.

PY - 2011/8/1

Y1 - 2011/8/1

N2 - 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.

AB - 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.

KW - Asymptotic quantization theory

KW - distributed source coding

KW - optimal point density function

KW - rate-distortion theory

UR - http://www.scopus.com/inward/record.url?scp=79955746919&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955746919&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2158882

DO - 10.1109/TIT.2011.2158882

M3 - Review article

AN - SCOPUS:79955746919

VL - 57

SP - 5298

EP - 5325

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 8

M1 - 5961835

ER -