Gaussian variable packet-error coding

We consider the problem of communicating a Gaussian source over several paths in a network, some unknown subset of which are subject to adversarial errors. The aim is to encode the source in such a way that one can provide a mean-square error distortion guarantee at the receiver that improves as the number of path-errors decreases. We show that a natural design based on error-correcting and error-detecting codes is not order-optimal in the rate as the distortion constraint tends to zero, but a hybrid scheme that involves a form of uncoded transmission is.