In this paper, we generalize the notion of unconstrained quantization of the
classical Cantor distribution to constrained quantization and give a general
definition of constrained quantization. Toward this, we calculate the optimal
sets of n-points, nth constrained quantization errors, the constrained
quantization dimensions, and the constrained quantization coefficients taking
different families of constraints for all nβN. The results in this
paper show that both the constrained quantization dimension and the constrained
quantization coefficient for the Cantor distribution depend on the underlying
constraints. It also shows that the constrained quantization coefficient for
the Cantor distribution can exist and be equal to the constrained quantization
dimension. These facts are not true in the unconstrained quantization for the
Cantor distribution.Comment: arXiv admin note: text overlap with arXiv:2305.1111