Bayesian quantized network coding via generalized approximate message passing

In this paper, we study message passing-based decoding of real network coded packets. We explain our developments on the idea of using real field network codes for distributed compression of inter-node correlated messages. Then, we discuss the use of iterative message passing-based decoding for the described network coding scenario, as the main contribution of this paper. Motivated by Bayesian compressed sensing, we discuss the possibility of approximate decoding, even with fewer received measurements (packets) than the number of messages. As a result, our real field network coding scenario, called quantized network coding, is capable of inter-node compression without the need to know the inter-node redundancy of messages. We also present our numerical and analytic arguments on the robustness and computational simplicity (relative to the previously proposed linear programming and standard belief propagation) of our proposed decoding algorithm for the quantized network coding.