The Impacts of Additive Noise and 1-bit Quantization on the Correlation Coefficient in the Low-SNR Regime
Adam R. Williamson · 2019
This paper analyzes the impact of 2-level (1-bit) quantization on the correlation of Gaussian sources and of binary sources in the presence of additive noise, with a focus on the low-SNR regime. In this regime, in which the correlation vanishes as the SNR tends to zero, 1-bit symmetric-threshold quantization of Gaussian sources and of equiprobable, antipodal binary sources degrades the correlation by 2/π(-1.96 dB), a result first established by Van Vleck for correlated Gaussian sources. Symmetric quantization of these sources also reduces the channel capacity per unit-energy by the same factor. However, asymmetric-threshold quantization of a class of binary source distributions known as flash signaling can avoid the 2/π penalty in channel capacity, as shown by Koch and Lapidoth. In this paper, we show how flash signaling with asymmetric quantization can not only avoid the 2/π penalty in correlation, but as the SNR tends to zero, the quantized correlation can approach the noise-free source correlation.