Interleaved optimization-quantization of reflection coefficients: OQ-Levinson-Durbin and OQ-Burg algorithms

In this paper we propose methods for obtaining the quantized reflection coefficients in an interleaved manner, where quantization alternates with optimization. The problem is relevant for the optimization involved when applying minimum description length principle for inference and also as a part of lossless coding schemes. It turns out that the recursive-in-order structure used in the optimal design of the linear predictors for nonquantized parameters is well suited for a greedy optimization-quantization (OQ) process. We introduce the optimization-quantization versions of two important algorithms: Levinson-Durbin algorithm and Burg algorithm and also discuss a direct least squares approach. The numerical results for the linear prediction with the proposed schemes show improvements in terms of mean square errors for audio signals. Results are also shown for the use of an OQ algorithm inside the MPEG-4 ALS lossless audio coder.