On minimum energy for robust Gaussian joint source-channel coding with a distortion-noise profile

Minimum energy required to achieve a distortion-noise profile, i.e., a function indicating the maximum allowed distortion value for each noise level, is studied for robust transmission of Gaussian sources over Gaussian channels. It is shown that for the inversely linear profile, uncoded transmission is optimal. On the other hand, it turns out that exponential profiles are not achievable with finite energy. Finally, using a family of lower bounds and a proposed coding scheme, the minimum energy behavior for the square-law profile is understood up to a multiplicative constant.