A Kalman filtering approach to GMM predictive coding of LSFS for packet loss conditions

Gaussian mixture model (GMM)-based vector quantization of line spectral frequencies (LSFs) has gained wide acceptance in speech coding. In predictive coding of LSFs, the GMM approach utilizing Kalman filtering principles to account for quantization noise has been shown to perform better than a baseline GMM recursive coder approaches for both clean and packet loss conditions at roughly the same complexity. However, the GMM Kalman based predictive coder was not specifically designed for operation in packet loss conditions. In this paper, we show how an initial GMM Kalman predictive coder can be utilized to obtain a robust GMM predictive coder specifically designed to operate in packet loss. In particular, we demonstrate how one can define sets of encoding and decoding modes, and design special Kalman encoding and decoding gains for each set. With this framework, GMM predictive coding design can be viewed as determining the special Kalman gains that minimize the expected minimum mean squared error at the decoder in packet loss conditions. The simulation results demonstrate that the proposed robust Kalman predictive coder achieves better performance than the baseline GMM predictive coders.