Hybrid Digital-Analog Transmission for the Gaussian One-Helper Problem

The one-helper joint source-channel coding problem, in which a main source is to be reconstructed with minimum distortion with the help of a correlated helper source, is studied. Focusing on the case of Gaussian sources and a Gaussian multiple access channel (MAC), a generalized hybrid digital-analog scheme is proposed, in which each user allocates its available power among the analog and digital signals and transmits a superposition of the two. It is shown that this generalized hybrid scheme reduces to pure analog or pure digital transmission depending on the system parameters. Finally, the optimal hybrid transmission strategy is identified analytically in certain special scenarios modeling legacy systems.