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In this paper, mathematical bases for non-adaptive joint source networkcoding of correlated messages in a Bayesian scenario are studied. Specifically,we introduce one-step Quantized Network Coding (QNC), which is a hybridcombination of network coding and packet forwarding for transmission. Motivatedby the work on Bayesian compressed sensing, we derive theoretical guarantees onrobust recovery in a one-step QNC scenario. Our mathematical derivations forGaussian messages express the opportunity of distributed compression by usingone-step QNC, as a simplified version of QNC scenario. Our simulation resultsshow an improvement in terms of quality-delay performance over routing basedpacket forwarding.

One-Step Quantized Network Coding for Near Sparse Gaussian Messages