Optimal quantization for noisy channels with random index assignment

Abstract

This paper studies the design of vector quantization (VQ) on noisy channels and its asymptotic performance analysis. Given a tandem source-channel coding system with VQ and block channel coding, we derive a closed-form formula of the average end-to-end distortion (EED), which reveals a structural factor called the scatter factor for noisy channel quantizers. Based on this formula, an iterative algorithm is developed for jointly designing optimal quantizers with channel conditions. Simulations show that quantizers that are jointly designed with channel conditions significantly reduce the EED when compared with quantizers that are designed separately from channel conditions. Indeed, our asymptotic analyses show that the infimum of the mean squared EED over all possible quantizers with joint quantization design is p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">err</sub> sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , where p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">err</sub> is the average transmission error probability of the channel and sigma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is the component variance of the source. This is 4.77dB better than that with separate quantization design for an i.i.d. Guassian source.