高斯多址信道在和速率面相对内部上的二阶渐近
Second-Order Asymptotics for the Gaussian MAC on the Relative Interior of the Sum-Rate Face
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中文总结 AI 辅助
该论文刻画了两用户高斯多址信道在和速率面相对内部上的二阶编码速率区域，证明非平凡混合功率分配优于恒定功率分配，并给出最优编码时间共享策略。
中文摘要 AI 辅助
我们在最大每码字功率约束下，完全刻画了在总和速率面的相对内部点上，两用户高斯多址信道的二阶编码速率区域。对于任意固定的平均错误概率 $0 < \varepsilon < 1/2$，功率分配的非平凡混合会降低和速率色散，并严格优于基于恒定功率分配的标准内界。因此，恒定功率分配虽然足以达到一阶容量区域，但在该机制下不足以实现二阶最优性。我们的可达性证明基于Scarlett、Martinez和Guillén i Fàbregas的恒定组合和编码时间共享框架，并对允许的功率分配进行优化。匹配的二阶逆定理证明了所得编码时间共享策略的最优性。
英文摘要
We completely characterize the second-order coding rate region of the two-user Gaussian multiple-access channel at points in the relative interior of the sum-rate face, under maximal per-codeword power constraints. For any fixed average error probability $0 < \varepsilon < 1/2$, a nontrivial mixture of power splits reduces the sum-rate dispersion and strictly improves upon standard inner bounds based on a constant power split. Thus, a constant power split, although sufficient to attain the first-order capacity region, is insufficient for second-order optimality in this regime. Our achievability proof builds on the constant composition and coded time-sharing framework of Scarlett, Martinez, and Guillén i Fàbregas, with an optimization over admissible power splits. A matching second-order converse establishes the optimality of the resulting coded time-sharing strategy.
发表机构
- National University of Singapore（新加坡国立大学）
机构由 AI 辅助整理，请以论文原文为准。
