Gaussian source coding based on variance-mismatched three-level scalar quantisation using Q-function approximations

This study deals with three-level scalar quantisation of a Gaussian source, followed by Huffman encoder, especially suitable for signal compression purposes. The variance-matched and variance-mismatched versions of quantiser are considered. Simple approximate closed-form expressions for performance evaluation in terms of signal-to-quantisation-noise ratio and bit rate are derived using the corresponding Q-function approximations. The accuracy of the derived formulas is tested using the relative error as a measure of performance. It is shown that the derived formulas for variance-matched (for a reference variance) and variance-mismatched (in a wide range of input signal variances) provide higher accuracy in comparison to baselines using other available Q-function approximations or available approximate formulas for non-uniform scalar quantisation of Gaussian source.