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首页> 外文期刊>Information Theory, IEEE Transactions on >Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions
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Distributed Scalar Quantization for Computing: High-Resolution Analysis and Extensions

机译：用于计算的分布式标量量化：高分辨率分析和扩展

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摘要

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.
机译：量化信息的传递通常伴随着计算。我们考虑了分布式功能标量量化的情况：（可能是相关的）源的分布式标量量化，然后是函数的集中计算。在源和函数的平滑条件下，开发了可扩展的标量量化器设计，以在允许增长量化器分辨率的同时最大程度地减少计算函数的均方误差（MSE）。相对于不考虑功能而设计的量化器，可以实现惊人的改进，并且在熵受限的设置中比在固定速率设置中更大。作为对基础分析的扩展，我们描述了一大类函数，这些函数可以满足常规量化的要求，考虑某些函数，这些函数可以在没有任意精细量化的情况下实现渐近最优性，并且允许源编码器之间的协作有限。在熵约束的设置中，编码器之间传递的每个样本单个位会对功能失真产生任意大的影响。相反，这种通信在固定速率设置中影响很小。

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