Asymptotic energy-distortion performance of zero- and low-delay transmission of Gaussian sources over energy-limited Gaussian channels is studied. A lower bound for the leading term in the negative logarithm of the distortion, termed the energy-distortion exponent , is derived through an achievable scheme based on high-resolution quantization 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 improved with respect to its naïve value, i.e., that achieved by optimizing purely the source coding performance instead of the end-to-end distortion. Lastly, a tradeoff of achievable energy-distortion exponents is derived for broadcast scenarios by extending the point-to-point scheme to include a successive refinement source coder coupled with two rounds of orthogonal signaling. A simple parametric computation algorithm is derived for the tradeoff.

中文翻译：

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高斯信道低时延传输能量失真权衡的渐近分析


研究了能量有限高斯信道上高斯源零时延和低时延传输的渐近能量失真性能。失真的负对数中首项的下界（称为能量失真指数）是通过基于高分辨率量化与正交信令相结合的可实现方案得出的。失真负对数中的高阶项（称为能量失真色散 ）经过优化，同时将首项（能量失真指数）保持在零延迟的最佳（分别是最著名）值（分别为低延迟）制度。与文献中先前报道的衰减色散相比，所提出的编码方案实现了恒定色散。当该方案被优化时，该常数可以相对于其原始值得到改进，即通过纯粹优化源编码性能而不是端到端失真来实现。最后，通过扩展点对点方案以包括与两轮正交信令耦合的连续细化源编码器，针对广播场景导出可实现的能量失真指数的权衡。导出了一个简单的参数计算算法来进行权衡。