A Novel Approximate Lloyd-max Quantizer and Its Analysis

Several distributed real-time signal sensing/monitoring systems require quantization for efficient signal representation. These distributed sensors often have computational and energy limitations. Motivated by this concern, we propose a novel quantization scheme called Approximate Lloyd-Max (ALM) that is nearly-optimal. Assuming a continuous and finite support probability distribution of the source, we show that our ALM quantizer converges to the classical Lloyd-Max quantizer with increasing bitrate. Our ALM quantizer, which is recursive, converges exponentially fast with the number of iteration. We illustrate our results using simulations for the Beta(4,2) distribution on the source.