Gaussian Mixture Kalman Predictive Coding of Line Spectral Frequencies

Gaussian mixture model (GMM)-based predictive coding of line spectral frequencies (LSFs) has gained wide acceptance. In such coders, each mixture of a GMM can be interpreted as defining a linear predictive transform coder. In this paper, we use Kalman filtering principles to model each of these linear predictive transform coders to present GMM Kalman predictive coding. In particular, we show how suitable modeling of quantization noise leads to an adaptive a posteriori GMM that defines a signal-adaptive predictive coder that provides improved coding of LSFs in comparison with the baseline recursive GMM predictive coder. Moreover, we show how running the GMM Kalman predictive coders to convergence can be used to design a stationary GMM Kalman predictive coding system which again provides improved coding of LSFs but now with only a modest increase in run-time complexity over the baseline. In packet loss conditions, this stationary GMM Kalman predictive coder provides much better performance than the recursive GMM predictive coder, and in fact has comparable mean performance to a memoryless GMM coder. Finally, we illustrate how one can utilize Kalman filtering principles to design a postfilter which enhances decoded vectors from a recursive GMM predictive coder without any modifications to the encoding process.