On transmission of multiple Gaussian sources over a Gaussian MAC using a VQLC mapping

In this paper we generalize an existing distributed zero-delay joint source-channel coding scheme for communication of a multivariate Gaussian on a Gaussian Multiple Access Channel named Distributed Quantization Linear Coder (DQLC) to arbitrary code length. Although the DQLC is well performing, it leaves a certain gap to the performance upper bound (or distortion lower bound) based on arbitrary code length. The purpose of this paper is to determine if the generalization of the DQLC to arbitrary code length, named Vector Quantization Linear Coder (VQLC), can close the gap to the bound when the code length is large. Our results show that the VQLC mapping has the potential to reach the upper bound for any number of Gaussian sources at high SNR when the sources are uncorrelated. We also approximately determine the VQLC performance as a function of code length for the special case of two sources.