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Codecell contiguity in optimal fixed-rate and entropy-constrained network scalar quantizers

We consider the properties of optimal fixed-rate and entropy-constrained scalar quantizers for finite alphabet sources. In particular, we consider conditions under which the optimal scalar quantizer with contiguous codecells achieves performance no worse than the optimal scalar quantizer without the constraint of codecell contiguity. In addition to traditional scalar quantizers, we consider multi-resolution scalar quantizers and multiple description scalar quantizers and also look briefly at codes with decoder side information (Wyner-Ziv codes). While the conditions under which codecell contiguity is consistent with optimality in fixed-rate and entropy-constrained scalar quantization are quite broad, even with the squared error distortion measure, codecell contiguity in fixed-rate and entropy-constrained multi-resolution, multiple description, and Wyner-Ziv scalar quantization can preclude optimality for some sources.