AI 中文总结
该研究针对离散Wyner-Ziv问题建立精确二阶渐近特性，推导二阶逆界并扩展Li和Li（arXiv 2025）的可达性结果，通过数值示例验证其可达性界在四元源场景下更优，可降低二阶编码率。
AI 中文摘要
我们重新研究离散Wyner-Ziv问题并建立其精确二阶渐近特性。我们的主要贡献是一个二阶逆界，该界通过后验分解、集中不等式以及鞅的条件高斯近似推导得出。此外，我们扩展了Li和Li（arXiv 2025）的先前最可达性结果，允许测试信道依赖于观测源序列的类型。通过结合我们的可达性界和逆界，建立了精确二阶渐近特性。特别地，我们表明Li和Li（arXiv 2025）的可达性界在一般情况下并非最优。具体而言，我们提供两个数值示例说明我们的结果：二元非对称源和四元源。对于第一个示例，Li和Li（arXiv 2025）的可达性界达到最优二阶渐近特性；但在第二个示例中，我们表明我们的可达性结果是最优的，在 excess-distortion 概率为0.1时，该结果将Li和Li（arXiv 2025）的二阶编码率降低10.77%，在 excess-distortion 概率为0.2时降低21.35%。
英文摘要
We revisit the discrete Wyner--Ziv problem and establish exact second-order asymptotics. Our main contribution is a second-order converse bound, which is derived using posterior decomposition, concentration inequalities, and a conditional Gaussian approximation for martingales. Furthermore, we extend the previous best known achievability result of Li and Li (arXiv 2025) by allowing the test channel to depend on the type of the observed source sequence. Exact second-order asymptotics are established by combining our achievability and converse bounds. In particular, we show that the achievability bound of Li and Li (arXiv 2025) is not optimal in general. Specifically, we provide two numerical examples to illustrate our results: a binary asymmetric source and a quaternary source. For the first example, the achievability bound of Li and Li (arXiv 2025) achieves the optimal second-order asymptotics. However, in the second example, we show that our achievability result is optimal, which reduces the second-order coding rate of Li and Li (arXiv 2025) by $10.77\%$ at the excess-distortion probability of $0.1$ and by $21.35\%$ at the excess-distortion probability of $0.2$.
