Low Rate Uniform Scalar Quantization of Memoryless Gaussian Sources

The low-rate (<;1 bits per sample) operational rate-distortion performance of uniform scalar quantizers for the memoryless Gaussian source is studied. Approximate analytical expressions for the operational rate-distortion function are derived, and the accuracy of the derived function is verified through simulation. It is shown that in the zero-rate limit the derived operational rate-distortion function is first-order optimal with respect to the Shannon lower bound. The derived function is used to study the performance of uniform scalar quantizers for the Gaussian Wyner-Ziv problem. Lastly, the derived low-rate rate-distortion function is used to provide improved low-rate bit allocation for jointly Gaussian vectors.