Distortion Lower Bounds for Finite Dimensional Joint Source-Channel Coding

In this work we consider joint source-channel coding (JSCC) schemes that are limited to work in blocks of finite length. We focus on the high resolution and high signal to noise ratio (SNR) regime, and derive new lower bounds for the distortion of JSCC schemes over r(th)-moment constrained additive noise channels. These new bounds are based on the method of Ziv and Zakai [11], combined with the Renyi information measure, as was recently proposed by Leibowitz and Zamir [5]. Numerical results are presented for the case of Gaussian source and channel, and it is shown that the new bounds improve upon Shannon's original bound in several cases, including bandwidth expansion and reduction.