How good is your index assignment?

Due to channel errors, index assignment is an important part of a VQ (vector quantization) design. It is shown that if the VQ is regarded as a transform of the hypercube spanned by the code words, the optimal index assignment for a full entropy encoder is the assignment that yields the most linear transform of the hypercube. Two fast and reliable methods of evaluating the inherent structure of a robust VQ without explicit knowledge about the training or the source are presented. The validity of the linearity measurement for encoders without full entropy is discussed. The significance of the measurements is demonstrated on VQs trained on speech and on synthetic sources.<>