Numerous voice, still image, audio, and video compression standards have been developed over the last 25 years, and significant advances in the state of the art have been achieved. However, in the more than 50 years since Shannon’s seminal 1959 paper, no rate distortion bounds for voice and video have been forthcoming. In this volume, we present the first rate distortion bounds for voice and vi...

Direct evaluation of the rate-distortion function has rarely been achieved when it is strictly greater than its Shannon lower bound. In this paper, we consider the rate-distortion function for the distortion measure defined by an ε-insensitive loss function. We first present the Shannon lower bound applicable to any source distribution with finite differential entropy. Then, focusing on the Lap...

We develop new rate distortion bounds for narrowband and wideband speech coding based on composite source models for speech and perceptual PESQ-MOS/WPESQ distortion measures. It is shown that these new rate distortion bounds do in fact lower bound the performance of important standardized speech codecs, including, G.726, G.727, AMR-NB, G.729, G.718, G.722, G.722.1, and AMR-WB. The approach is t...

Kernel methods have been used for turning linear learning algorithms into nonlinear ones. These nonlinear algorithms measure distances between data points by the distance in the kernel-induced feature space. In lossy data compression, the optimal tradeoff between the number of quantized points and the incurred distortion is characterized by the rate-distortion function. However, the rate-distor...

The in-training-set performance of a vector quantizer as a function of its training set size is investigated. For squared error distortion and independent training data, worst case type upper bounds are derived on the minimum training distortion achieved by an empirically optimal quantizer. These bounds show that the training distortion can underestimate the minimum distortion of a truly optima...

In this paper, we introduce new lower bounds on the distortion of scalar fixedrate codes for lossy compression with side information available at the receiver. These bounds are derived by presenting the relevant random variables as a Markov chain and applying generalized data processing inequalities a la Ziv and Zakai. We show that by replacing the logarithmic function with other functions, in ...

We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed sources in the finite block-length regime. Based on the convex optimization framework of the rate-distortion theory, we derive a lower bound on the quantization distortion under finite block-length, which is shown to be greater than the asymptotic distortion given by the ratedis...