On Asymptotic Analysis of Energy-Distortion Tradeoff for Low-Delay Transmission over Gaussian Channels

Asymptotic energy-distortion performance of zero- and low-delay communication scenarios under additive white Gaussian noise (AWGN) is investigated. Using high-resolution analysis for quantizer design coupled with orthogonal signaling, the higher-order term in the negative logarithm of the distortion, termed the energy-distortion dispersion, is optimized while keeping the leading term, the energy-distortion exponent, at its optimal (respectively, the best known) value, for the zero-delay (respectively, low-delay) regime. In contrast with the decaying dispersion previously reported in the literature, the proposed coding scheme achieves a constant dispersion. When the scheme is optimized, this constant can be increased considerably with respect to its naive value, i.e., that achieved by optimizing purely the source coding performance instead of the end-to-end distortion.