Analysis and optimization of distributed linear coding of Gaussian sources

Recent work has shown that compressed sensing can be successfully applied in distributed scenarios. In this framework, we study the exploitation of the correlation statistics in the encoding and recovery processes for independently transmitted Gaussian correlated sources, obtaining the optimal projection matrices in the MMSE sense. Encoding is performed separately for each source using either random or the aforementioned optimized projections. The effect of correlation and noise on the achievable rates obtained through MMSE estimation is studied analytically. Simulation results show a perfect match with the MMSE analysis.