In many resource allocation problems, a centralized controller needs to award some resource to a user selected from a collection of distributed users with the goal of maximizing the utility the user would receive from the resource. This can be modeled as the controller computing an extremum of the distributed users’ utilities. The overhead rate necessary to enable the controller to reproduce the users’ local state can be prohibitively high. An approach to reduce this overhead is interactive communication wherein rate savings are achieved by tolerating an increase in delay. In this paper, we consider the design of a simple achievable scheme based on successive refinements of scalar quantization at each user. The optimal quantization policy is computed via a dynamic program and we demonstrate that tolerating a small increase in delay can yield significant rate savings. We then consider two simpler quantization policies to investigate the scaling properties of the rate-delay tradeoffs. Using a combination of these simpler policies, the performance of the optimal policy can be closely approximated with lower computational costs.
A concern of signal processing is to provide optimized practical quantization algorithms for the DFC system with performance close to the rate-distortion limits @cite_9 @cite_13 @cite_17 @cite_33 @cite_11 @cite_5 @cite_6 . There are asymptotic results for sufficiently high-rate and low-distortion that are derived by applying high rate quantization theory @cite_16 , while there are also non-asymptotic results derived from generalizations of Lloyd's algorithm.
@cite_33 @cite_9 @cite_17 @cite_6 @cite_5 @cite_16 @cite_13 @cite_11
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As communication systems scale up in speed and bandwidth, the cost and power consumption of high-precision (e.g., 8-12 bits) analog-to-digital conversion (ADC) becomes the limiting factor in modern transceiver architectures based on digital signal processing. In this work, we explore the impact of lowering the precision of the ADC on the performance of the communication link. Specifically, we evaluate the communication limits imposed by low-precision ADC (e.g., 1-3 bits) for transmission over the real discrete-time additive white Gaussian noise (AWGN) channel, under an average power constraint on the input. For an ADC with K quantization bins (i.e., a precision of log2 K bits), we show that the input distribution need not have any more than K+1 mass points to achieve the channel capacity. For 2-bin (1-bit) symmetric quantization, this result is tightened to show that binary antipodal signaling is optimum for any signal-to- noise ratio (SNR). For multi-bit quantization, a dual formulation of the channel capacity problem is used to obtain tight upper bounds on the capacity. The cutting-plane algorithm is employed to compute the capacity numerically, and the results obtained are used to make the following encouraging observations : (a) up to a moderately high SNR of 20 dB, 2-3 bit quantization results in only 10-20 reduction of spectral efficiency compared to unquantized observations, (b) standard equiprobable pulse amplitude modulated input with quantizer thresholds set to implement maximum likelihood hard decisions is asymptotically optimum at high SNR, and works well at low to moderate SNRs as well. The quantization of the observed data for sequential signal detection is studied. The criteria used are the minimizations of the average sample number under the hypothesis, the average sample number under the alternative, and the maximum average sample number. Numerical results show that the performance is not very sensitive to different criteria. Using a sequential probability ratio test (SPRT), the performances of optimum quantizers are compared to systems with unquantized data. The asymptotic relative efficiencies of the quantizerSPRT's with respect to the SPRT for unquantized data are derived for symmetric noise densities. The relation between these asymptotic relative efficiencies and those of fixed-sample-size detectors is noted. This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a difference in how fast their minimum achievable coding rates approach the rate-distortion function, providing yet another example where at finite blocklengths one must put aside traditional asymptotic thinking. This correspondence analyzes the low-resolution performance of entropy-constrained scalar quantization. It focuses mostly on Gaussian sources, for which it is shown that for both binary quantizers and infinite-level uniform threshold quantizers, as D approaches the source variance spl sigma sup 2 , the least entropy of such quantizers with mean-squared error D or less approaches zero with slope -log sub 2 e 2 spl sigma sup 2 . As the Shannon rate-distortion function approaches zero with the same slope, this shows that in the low-resolution region, scalar quantization with entropy coding is asymptotically as good as any coding technique.