如何计算模素幂和？
How to Compute Modulo Prime-Power Sums ?
摘要：
介绍了一类新的结构码-准群码（QGC）. QGC是组码的子集。与组码不同，QGC在组添加下不关闭。可以选择QGC的参数，使得$\mathcal{C}+\mathcal{C}$的大小等于$|\mathcal{C}|$和$|\mathcal{C}|^2$之间的任何数。我们分析了一类特定的QGC的性能。这类QGC是通过将单字母分布分配给群码中码字的索引来构造的。然后，QGC被定义为一组码字，其索引是在对应于这些单字母分布的典型集合。这类QGC的渐近性能极限的特点是使用单字母信息量。相应的覆盖和包装界推导。它表明，点对点信道容量和最佳率失真函数是可以实现的使用QGC。基于QGC的编码策略介绍了三个基本的多终端问题：Körner-Marton问题的模素幂和，计算多址信道（MAC），MAC与分布式状态。对于每个问题，一个单字母可实现的速率区域推导。通过实例表明，该编码策略是对以往基于非结构码、线性码和分组码的编码策略的改进。
英文摘要：
A new class of structured codes called Quasi Group Codes (QGC) is introduced. A QGC is a subset of a group code. In contrast with group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen such that the size of $\mathcal{C}+\mathcal{C}$ is equal to any number between $|\mathcal{C}|$ and $|\mathcal{C}|^2$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions. The asymptotic performance limits of this class of QGCs is characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Körner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on unstructured codes, linear codes and group codes.
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