An Information-Theoretic Framework for Receiver Quantization in Communication

2025-05-18

AI Summary

This work investigates the fundamental impact of low-resolution quantization at the receiver on the information-theoretic limits of communication systems. To characterize the performance degradation arising from coarse quantization, we develop a generalized mutual information (GMI)-based achievable rate framework. We establish, for the first time, an exact logarithmic relationship between quantization rate loss and minimum mean-square error (MMSE): $log(1+gammacdot ext{SNR})$. We prove theoretically that the optimal loading factor simultaneously maximizes GMI and minimizes MMSE, and derive its asymptotic closed-form expression. Furthermore, we uncover the geometric essence of uniform quantization and rigorously show that GMI–MMSE consistency holds exclusively under this quantization scheme. Our analysis integrates complex Gaussian codebooks, symmetric quantizers, nearest-neighbor decoding, and asymptotic methods. The results provide both theoretical foundations and performance benchmarks for the design of low-precision receivers.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We investigate information-theoretic limits and design of communication under receiver quantization. Unlike most existing studies, this work is more focused on the impact of resolution reduction from high to low. We consider a standard transceiver architecture, which includes i.i.d. complex Gaussian codebook at the transmitter, and a symmetric quantizer cascaded with a nearest neighbor decoder at the receiver. Employing the generalized mutual information (GMI), an achievable rate under general quantization rules is obtained in an analytical form, which shows that the rate loss due to quantization is $logleft(1+gammamathsf{SNR} ight)$, where $gamma$ is determined by thresholds and levels of the quantizer. Based on this result, the performance under uniform receiver quantization is analyzed comprehensively. We show that the front-end gain control, which determines the loading factor of quantization, has an increasing impact on performance as the resolution decreases. In particular, we prove that the unique loading factor that minimizes the MSE also maximizes the GMI, and the corresponding irreducible rate loss is given by $logleft(1+mathsf {mmse}cdotmathsf{SNR} ight)$, where mmse is the minimum MSE normalized by the variance of quantizer input, and is equal to the minimum of $gamma$. A geometrical interpretation for the optimal uniform quantization at the receiver is further established. Moreover, by asymptotic analysis, we characterize the impact of biased gain control, including how small rate losses decay to zero and achievable rate approximations under large bias. From asymptotic expressions of the optimal loading factor and mmse, approximations and several per-bit rules for performance are also provided. Finally we discuss more types of receiver quantization and show that the consistency between achievable rate maximization and MSE minimization does not hold in general.

Problem

• Study impact of receiver quantization resolution reduction
• Analyze achievable rate loss under uniform quantization
• Explore optimal gain control for quantization performance

Innovation

• Uses generalized mutual information for quantization analysis
• Analyzes uniform receiver quantization performance comprehensively
• Links MSE minimization with achievable rate maximization