Transform coding is central to standards for audio, image and video coding. In conventional transform coding, the encoder first performs a linear transformation, followed by uniform scalar quantization and scalar entropy coding. With scalar quantization, to minimize the distortion at high rate, the best one can hope for is a quantizer that partitions into hypercubes; and with scalar entropy coding, one desires independent transform coefficients to minimize the rate. Transform coding has a clean analytical theory for Gaussian sources because these two virtues can be achieved simultaneously.