论文标题
关于$ k $ - 接收器广播频道的可实现率区域，通过详尽的消息分裂
On the Achievable Rate Region of the $ K $-Receiver Broadcast Channels via Exhaustive Message Splitting
论文作者
论文摘要
本文重点介绍了$ k $ -Receiver离散时间无内存广播频道（DM-BC），并带有私人消息，发射器希望分别向$ k $ kum接收器传达$ k $私人消息。根据详尽的消息分裂和$ k $级的修改后的Marton的编码，提出了对容量区域的一般内部界限。关键的想法是将每条消息分为$ \ sum_ {j = 1}^k {k \ select j} $ castessages每个对应于分配的用户恢复它们的用户，然后通过彼此共同典型的代码字发送这些提交。为了确保所有传输的代码字的共同典型性，子编码书大小的足够条件是通过新建立的层次结构覆盖引理来得出的，该分层覆盖了引理，该层次扩展了$ K $ level的2级多变量覆盖Lemma，包括$（2^{k} -1）$随机变量，并与更古代的相关性。由于辅助随机变量的数量和速率约束都以$（2^{k} -1）$线性增加，因此，当$ k $大时，标准的傅立叶 - 摩托群消除过程变得不可行。为了解决这个问题，我们通过对构成$ \ {1，\ dots，k \} $的功率集的集合的特殊观察，获得了可实现速率区域的最终形式。所提出的可实现的速率区域允许任意输入概率质量函数（PMF），并以$ k $ -Receiver（$ k \ geq 3 $）的所有先前已知的质量函数（PMF）改进，其输入PMF应满足某些Markov链（S）。
This paper focuses on $ K $-receiver discrete-time memoryless broadcast channels (DM-BCs) with private messages, where the transmitter wishes to convey $K$ private messages to $K$ receivers respectively. A general inner bound on the capacity region is proposed based on an exhaustive message splitting and a $K$-level modified Marton's coding. The key idea is to split every message into $ \sum_{j=1}^K {K\choose j} $ submessages each corresponding to a set of users who are assigned to recover them, and then send these submessages through codewords that are jointly typical with each other. To guarantee the joint typicality among all transmitted codewords, a sufficient condition on the subcodebooks sizes is derived through a newly establishing hierarchical covering lemma, which extends the 2-level multivariate covering lemma to the $K$-level case including $(2^{K}-1)$ random variables with more intricate dependence. As the number of auxiliary random variables and rate constraints both increase linearly with $(2^{K}-1)$, the standard Fourier-Motzkin elimination procedure becomes infeasible when $K$ is large. To tackle this problem, we obtain the final form of achievable rate region with a special observation of disjoint unions of sets that constitute the power set of $ \{1,\dots,K\}$. The proposed achievable rate region allows arbitrary input probability mass functions (pmfs) and improves over all previously known ones for $ K$-receiver ($K\geq 3$) BCs whose input pmfs should satisfy certain Markov chain(s).
