Performance of low rate entropy-constrained scalar quantizers

The operational rate-distortion function of entropy-constrained scalar quantizers in the asymptotic low resolution regime, for memoryless Gaussian sources, is investigated. It is shown that asymptotically, as distortion tends to variance, or equivalently as rate tends to zero, the operational rate-distortion function matches the Shannon rate-distortion function. This implies that scalar quantization is asymptotically optimal, a fact not previously known.