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The Asymptotic Solutions of the Capacity Maximal Quantization Problem

This paper proposes approximation approaches to the problem of finding optimal quantization schemes that maximize the mutual information of Gaussian channels, by deriving asymptotic solutions that are simple and analytical. Two major results are presented: i) we derived an approximation scheme with its quantization thresholds linearly depending on the standard deviation of noise, which has negligible loss on the entire range of the signal-to-noise ratio (SNR) for 2-PAM modulated channels; ii) based on the high-rate limit, we derived a simple estimator of the relative capacity loss, which is inversely proportional to the square of the number of quantization intervals. These solutions can potentially reduce the complexity of the design and implementation process of quantization schemes.