A Unifying Order-Theoretic Framework for Superposition Coding: Polymatroidal Structure and Optimality in the Multiple-Access Channel With General Message Sets
A Unifying Order-Theoretic Framework for Superposition Coding: Polymatroidal Structure and Optimality in the Multiple-Access Channel With General Message Sets
复制标题
叠加编码的统一阶理论框架：通用消息集多路访问信道中的多拟阵结构和最优性
DOI：
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发表时间：
2017
影响因子：
2.5
通讯作者：
M. Varanasi
中科院分区：
文献类型：
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作者：
Henry P. Romero;M. Varanasi
两种不同的随机编码技术，在文献中都被称为叠加编码，已被广泛用于获取各种通信网络容量区域的内界。其中一种是独立生成辅助码字，另一种是以依赖方式生成辅助码字。以具有通用消息集的多址信道为例，我们将这两种技术置于一个通用的顺序理论框架下。这个框架的关键属性是，它明确地说明了可能的辅助码字依赖的无环方向和传递性，导致三个重要的发现。首先，相对于固定的编码分布，通过依赖辅助码字生成的叠加编码可实现的速率集形成一个多边形，从而推广了具有独立辅助码字的叠加编码的相同已知结果。其次，我们通过混合产生依赖和独立的辅助码字，得到了一大类叠加编码方案，并证明了在每种情况下组成的多面体可达率区域也是多拟体。第三个发现是，在具有通用消息集的多址信道中，每个相关的叠加编码内界都达到容量区域。这些结果证明了辅助码字生成中依赖关系的复杂性与将它们映射到传输码字的函数的复杂性之间的权衡。
Two different random coding techniques, both referred to as superposition coding in the literature, have been widely used to obtain inner bounds for the capacity regions of various communication networks. In one, auxiliary codewords are generated independently, and in the other, they are generated in a dependent manner. Using the multiple-access channel with general message sets as a case study, we place the two techniques under a common, order-theoretic framework. The key attribute of this framework is that it explicitly accounts for the acyclic direction and transitivity of the possible auxiliary codeword dependencies, leading to three significant discoveries. First, with respect to a fixed coding distribution, the set of rates achievable by superposition coding with dependent auxiliary codeword generation forms a polymatroid, thereby generalizing the same previously known result for superposition coding with independent auxiliary codewords. Second, we obtain a large class of superposition coding schemes by intermingling dependent and independent auxiliary codeword generation, and demonstrate that the constituent polyhedral achievable rate regions are also polymatroids in each case. The third discovery is that, in the multiple-access channel with general message sets, each associated superposition coding inner bound attains the capacity region. These results demonstrate a tradeoff between the complexity of dependencies in auxiliary codeword generation and that of the function that maps them into transmitted codewords.