Abstract-This correspondence analyzes the low-resolution performance of entropy-constrained scalar quantization. It focuses mostly on Gaussian sources, for which it is shown that for both binary quantizers and infinitelevel uniform threshold quantizers, as approaches the source variance , the least entropy of such quantizers with mean-squared error or less approaches zero with slope . As the Shannon rate-distortion function approaches zero with the same slope, this shows that in the lowresolution region, scalar quantization with entropy coding is asymptotically as good as any coding technique. Index Terms-Entropy constrained quantization, Gaussian, low rate, low resolution, scalar quantization, squared error. This correspondence focuses on the rate-distortion performance of scalar quantization in the low-resolution regime where rate is small. While there are well known, asymptotically accurate, closed-form formulas for the rate-distortion performance of a variety of quantization schemes in the high resolution, i.e., high-encoding rate, regime, there is a shortage of similar formulas for the low resolution, i.e., low rate, regime. As a step in this direction, this correspondence focuses on scalar quantization with entropy coding and squared error distortion
There do exist special input pdf's for which entropy coding approaches the RD function REF in the low-rate limit, but the low-rate regime is challenging in general.
Low-resolution scalar quantization for Gaussian sources and squared error
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics