Distributed scalar quantization for computing: High-resolution analysis and extensions
Author(s)Misra, Vinith; Goyal, Vivek K.; Varshney, Lav Raj
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Research Laboratory of Electronics
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Misra, Vinith, Vivek K. Goyal, and Lav R. Varshney. “Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions.” IEEE Transactions on Information Theory 57.8 (2011): 5298–5325.
Author's final manuscript