Quantization with an adjustable codeword length penalty

Quantizers are generally designed either for fixed-rate coding or variable-rate coding. Under common conditions, variable-rate quantization leads to the same mean distortion for all quantization cells whereas fixed-rate is associated with a fixed bit allocation for each quantization operation. We show that both are special cases of the solution of a more general constraint that facilitates a practical trade-off between mean rate and rate outliers and mean distortion and outliers in distortion. The proposed constraint weights the code-word lengths exponentially. The resulting quantizers are suitable for commonly occurring scenarios such as those where a limited variability in rate can be tolerated by the network, those where the signal model may not be accurate, and those where source redundancy is used to counter channel errors.