Rate-distortion performance in coding bandlimited sources by sampling and dithered quantization

The rate-distortion characteristics of a scheme for encoding continuous-time band limited stationary sources, with a prescribed band, is considered. In this coding procedure the input is sampled at Nyquist´s rate or faster, the samples undergo dithered uniform or lattice quantization, using subtractive dither, and the quantizer output is entropy-coded, The rate-distortion performance, and the tradeoff between the sampling rate and the quantization accuracy is investigated, utilizing the observation that the coding scheme is equivalent to an additive noise channel. It is shown that the mean-square error of the scheme is fixed as long as the product of the sampling period and the quantizer second moment is kept constant, while for a fixed distortion the coding rate generally increases when the sampling rate exceeds the Nyquist rate. Finally, as the lattice quantizer dimension becomes large, the equivalent additive noise channel of the scheme tends to be white Gaussian, and both the rate and the distortion performance become invariant to the sampling rate