Towards entropy constrained lattice vector quantization

In most of the quantization applications, we need variable rate vector quantizers. In 1988, Chou, Lookabaugh and Gray designed vector quantizers having minimum distortion subject to an entropy constraint. For this purpose, they used a generalization of Lloyd algorithm to n dimensions, called the ECVQ algorithm. We propose to use lattices in order to design entropy constrained lattice vector quantizers (ECLVQ). Low resolution (nonasymptotical) distortion and rate approximation models are given and a generalization of the distortion formula to entropy constraint is formulated. These works generalize those of Gibson (see IEEE Trans. on Inform. Theory, vol.IT-39, no.3, p.786-804, 1993) on fixed rate quantizers, to any cubic lattice Zⁿ subject to entropy constraint