Minimum mean square error quantizers with uncorrelated input and quantization noise

Scalar quantizers with the minimum mean square error are designed in the case where the input signal and the quantization noise are uncorrelated. The probability density function (pdf) of the stochastic signal is assumed to be known. This design is then generalized to vector quantizers in the case where the expected value of the inner product between the input and quantization noise vector are equal to zero. The results show that the representation levels of the proposed quantizers are scaled versions of the representation levels of the well-known pdf optimized quantizers. The proposed quantizers are useful in subband coding applications.