高斯信源在块擦除信道上的联合信源信道编码：非渐近界与信道一致正态近似

中文摘要 AI 辅助

我们研究在过量均方失真准则下，高斯无记忆信源通过无记忆、可能非平稳的块擦除信道的有限块长有损传输问题。我们推导了可计算的非渐近可达性和逆界，并建立了匹配的三阶、信道一致正态近似。我们的非渐近可达性界源于对特定随机编码方案的系综平均过量失真概率的精确评估，并改进了使用相同信道输入和信源再现分布评估的已知一般一次性界（Kostina-Verdú 2013, Li-Anantharam 2021）。我们的非渐近逆论证以擦除模式为条件，并结合了能量条件球冠界与体积界。球冠论证保留了识别逆三阶项所需的几何前因子。在我们的信道一致正态近似中，我们表明对于固定的失真比、目标过量失真概率和块大小，所需的信源块长和余项常数与信道块长和擦除概率分布无关。充分和必要的信息平衡条件都包含项 $\frac12\log k$，其中 $k$ 是信源块长，并且仅在有限余项上有所不同。该分析结合了信源能量函数的阈值一致正态近似、逻辑和指数随机阈值表示，以及信道信息的信源诱导高斯平滑。数值评估将非渐近界与其常见的三阶正态近似进行了比较。我们的结果为使用少量数据包传输高维信源提供了基准。

英文摘要

We study finite-blocklength lossy transmission of a Gaussian memoryless source over memoryless, possibly nonstationary block erasure channels under an excess mean-squared distortion criterion. We derive computable nonasymptotic achievability and converse bounds and establish matching third-order, channel-uniform normal approximations. Our achievability bound exactly evaluates the ensemble-average excess-distortion probability of a specified random coding scheme and improves corresponding specializations of known general one-shot bounds. Our converse conditions on the erasure pattern and source energy and combines spherical-cap and volume bounds, with the spherical-cap term providing the geometric prefactor needed for the matching third-order term. In our channel-uniform normal approximation, we show that for fixed distortion ratio, target excess-distortion probability, and block size, the sufficient and necessary information-balance conditions have the same dispersion and $\frac{1}{2}\log k$ terms, where $k$ is the source blocklength, and differ only by bounded remainders that are uniform over the channel blocklength and erasure-probability profile. Numerical evaluations compare the nonasymptotic JSCC bounds and their common third-order normal approximation with an optimized symmetrized SSCC achievability benchmark.

发表机构

• Nokia Bell Labs（诺基亚贝尔实验室）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

Added an SSCC achievability benchmark and expanded numerical results