On the Performance of Vector Quantization under Constraint of Complexity Functionals

This work introduces mathematical properties for functionals that evaluate the complexity of vector quantization. Considering complexity functionals with such properties, it is shown that fundamental limits hold for the quantization trade-off between distortion, rate, and complexity. Part of the discussion presented in 2008 by Gray et al., [6], is extended, by replacing the original log codebook size constraint by a generalized complexity functional constraint.