论文标题
在最大失真下进行功能计算功能计算的源代码
Hypergraph-based Source Codes for Function Computation Under Maximal Distortion
论文作者
论文摘要
这项工作调查了最大畸变的功能源编码问题，这是由许多现代应用中近似功能计算的动机。最大失真将函数值的不精确重建视为完美计算，如果偏差小于公差水平，同时将重建的重建程度远大于该水平，则其差异为失败。使用对最大失真的几何理解，我们为功能计算提出了一种基于超图的源编码方案，该方案具有建设性的意义，即它提供了一个明确的过程，可以找到最佳或良好的辅助随机变量。此外，我们发现，基于超图的编码方案在用侧面信息进行计算的设置中实现了最佳速率 - 延伸功能，并在设置分布式计算源编码的设置中实现了berger-tung-tung-tung sum-rate内部界限。它还可以实现用于计算的多个描述编码的EL Gamal-Cover内部绑定，并且对于连续的完善和级联多重描述问题是最佳的。最后，显示了一类马尔可夫来源的查找正向测试渠道的复杂性降低的好处。
This work investigates functional source coding problems with maximal distortion, motivated by approximate function computation in many modern applications. The maximal distortion treats imprecise reconstruction of a function value as good as perfect computation if it deviates less than a tolerance level, while treating reconstruction that differs by more than that level as a failure. Using a geometric understanding of the maximal distortion, we propose a hypergraph-based source coding scheme for function computation that is constructive in the sense that it gives an explicit procedure for finding optimal or good auxiliary random variables. Moreover, we find that the hypergraph-based coding scheme achieves the optimal rate-distortion function in the setting of coding for computing with side information and achieves the Berger-Tung sum-rate inner bound in the setting of distributed source coding for computing. It also achieves the El Gamal-Cover inner bound for multiple description coding for computing and is optimal for successive refinement and cascade multiple description problems for computing. Lastly, the benefit of complexity reduction of finding a forward test channel is shown for a class of Markov sources.
