$M$ -Description Lattice Vector Quantization: Index Assignment and Analysis

In this paper, we investigate the design of symmetric entropy-constrained multiple description lattice vector quantization (MDLVQ), more specifically, MDLVQ index assignment. We consider a fine lattice containing clean similar sublattices with
S
-similarity. Due to the
S
-similarity of the sublattices, an
M
-fraction lattice can be used to regularly partition the fine lattice with smaller Voronoi cells than a sublattice does. With the partition, the MDLVQ index assignment design can be translated into a transportation problem in operations research. Both greedy and general algorithms are developed to pursue optimality of the index assignment. Under high-resolution assumption, we compare the proposed schemes with other relevant techniques in terms of optimality and complexity. Following our index assignment design, we also obtain an asymptotical close-form expression of
k
-description side distortion. Simulation results on coding different sources of Gaussian, speech and image are presented to validate the effectiveness of the proposed schemes.