On the 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 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. We introduce an outage concept, and analyze the expected distortion conditioned on no outage. We show that the proposed scheme can approach to the asymptotical decay for large enough energy for arbitrary outage probability. The proposed scheme builds on separation of source and channel coding, whereby the source is quantized with a high-resolution optimal quantizer. In the high energy-to-noise ratio (ENR) regime, the minimum energy required to obtain a given distortion level in the proposed scheme can approach arbitrarily close the Shannon bound, which can only be achieved using infinite delay.