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 $\log\left(1+\gamma\mathsf{SNR}\right)$, 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 $\log\left(1+\mathsf {mmse}\cdot\mathsf{SNR}\right)$, 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, showing how small rate losses decay to zero and providing 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.

翻译：我们研究了接收机量化下通信的信息论极限与系统设计。与大多数现有研究不同，本文更侧重于从高分辨率到低分辨率转换带来的影响。我们考虑一种标准的收发机架构，包括发射端的独立同分布复高斯码本，以及接收端级联的对称量化器与最近邻解码器。利用广义互信息（GMI），我们以解析形式得到了通用量化规则下的可达速率，该结果表明量化导致的速率损失为 $\log\left(1+\gamma\mathsf{SNR}\right)$，其中 $\gamma$ 由量化器的阈值与量化电平决定。基于此结果，我们全面分析了均匀接收机量化下的性能。研究表明，前端增益控制（决定量化负载因子）对性能的影响随分辨率降低而增强。特别地，我们证明了最小化均方误差的唯一负载因子同样能最大化GMI，且对应的不可约速率损失为 $\log\left(1+\mathsf {mmse}\cdot\mathsf{SNR}\right)$，其中mmse为量化器输入方差归一化的最小均方误差，且等于 $\gamma$ 的最小值。我们进一步建立了接收机最优均匀量化的几何解释。此外，通过渐近分析，我们刻画了偏置增益控制的影响，展示了小速率损失如何衰减至零，并给出了大偏置下的速率近似表达式。基于最优负载因子与mmse的渐近公式，我们还提供了性能近似表达式及若干按比特性能准则。最后，我们讨论了更多类型的接收机量化方案，并指出可达速率最大化与均方误差最小化的一致性在一般情况下并不成立。