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

Abstract: This paper provides lower bounds on the reconstruction error for transmission of two continuous correlated random vectors sent over both sum and parallel channels using the help of two causal feedback links from the decoder to the encoders connected to each sensor. This construction is considered for both uniformly and normally distributed sources with zero mean and unit variance. Additionally, a two-way retransmission protocol, which is a non-coherent adaptation of the original work by Yamamoto is introduced for an additive white Gaussian noise channel with one degree of freedom. Furthermore, the novel protocol of a single source is extended to the dual-source case again for two different source distributions. Asymptotic optimality of the protocols are analyzed and upper bounds on the distortion level are derived for two-rounds considering two extreme cases of high and low correlation among the sources. It is shown by both the upper and lower-bounds that collaboration can be achieved through energy accumulation. Analytical results are supported by numerical analysis for both the single and dual-source cases to show the improvement in terms of distortion to be gained by retransmission subject to the average energy used by protocol . To cover a more realistic scenario, the same protocol of a single source is adapted to a wireless channel and their performances are compared through numerical evaluation.