Two forward adaptive dual-mode companding scalar quantizers for Gaussian source

In this paper we propose a novel model of piecewise linear companding scalar quantizer (PLCSQ) having the piecewise linear compressor function determined by minimizing the mean-squared error between the optimal compressor function and the piecewise linear compressor function for the Gaussian source subject to the constraint of the equal number of cells per segments. We show that with the increase of the number of segments, the difference between the optimal compressor function and the novel piecewise linear compressor function decreases, which implies that the novel PLCSQ, having a simpler design and implementation procedure compared to the one of optimal companding scalar quantizer (OCSQ), can be used as a good alternative for OCSQ. We also consider the implementation of these two quantizers in the forward adaptive dual-mode quantization scheme. The numerical results presented in the paper indicate that the proposed quantizers are worth implementing not only in view of flexibility in the bit rate choice, but also in view of the significant gain in signal to quantization noise ratio (SQNR) achieved over the one forward adaptive unrestricted companding scalar quantizer. Also, the numerical results indicate great possibilities for application of the proposed quantizers in high-quality quantization of Gaussian source signals.