On the asymptotic distortion-energy tradeoff for zero-delay transmission of a Gaussian source over the AWGN channel

An achievable scheme for zero-delay transmission of an i.i.d. Gaussian source over an additive white Gaussian noise channel with no bandwidth limitation is introduced, and its energy-distortion performance is analyzed. By the nature of the problem, one must transmit each source sample separately but can use the channel infinitely many times. The proposed scheme builds on separation of source and channel coding, whereby the source is quantized into “equiprobable” cells so that the output can be seen as a message suitable for channel coding. Moreover, as the number of quantization cells go to infinity, the channel capacity can be approached with arbitrarily small error. In the high energy-to-noise ratio regime, the minimum energy required to obtain a given distortion level in the proposed scheme can come as close as 3dB to the Shannon bound, which can only be achieved using infinite delay.