Flexible Multiple Description Lattice Vector Quantizer with $L\geq 3$ Descriptions

In previous work on multiple description lattice vector quantizers (MDLVQ) with $L\geq 3$ descriptions, once the central and side lattice codebooks are fixed, the decoding quality is determined for all numbers $k$ of received descriptions. Therefore, it is not possible to achieve tradeoffs between the quality of reconstruction for different values of $k, 1\leq k\leq L-1$. This work proposes a flexible MDLVQ capable of overcoming the above drawback. For this, a different reconstruction method is employed and a heuristic index assignment algorithm, which uses $L-2$ parameters to control the distortions for $2\leq k\leq L-1$, is developed. The second contribution of this work is a structured index assignment for the case $L=3$ and the derivation of asymptotical expressions of the distortions at high resolution. The proposed index assignment has a simple mechanism for controlling the tradeoff between the reconstruction quality when $k=1$ and when $k=2$, and is able to achieve a wide range of distortion values.