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This paper provides lower bounds on the reconstruction error for transmissionof two continuous correlated random vectors sent over both sum and parallelchannels using the help of two causal feedback links from the decoder to theencoders connected to each sensor. This construction is considered for bothuniformly and normally distributed sources with zero mean and unit variance.Additionally, a two-way retransmission protocol, which is a non-coherentadaptation of the original work by Yamamoto is introduced for an additive whiteGaussian noise channel with one degree of freedom. Furthermore, the novelprotocol of a single source is extended to the dual-source case again for twodifferent source distributions. Asymptotic optimality of the protocols areanalyzed and upper bounds on the distortion level are derived for two-roundsconsidering two extreme cases of high and low correlation among the sources. Itis shown by both the upper and lower-bounds that collaboration can be achievedthrough energy accumulation. Analytical results are supported by numericalanalysis for both the single and dual-source cases to show the improvement interms of distortion to be gained by retransmission subject to the averageenergy used by protocol . To cover a more realistic scenario, the same protocolof a single source is adapted to a wireless channel and their performances arecompared through numerical evaluation.

Distortion bounds and Two-Way Protocols for One-Shot Transmission of Correlated Random Variables