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Generalized Lexicographic Products and the Index Coding Capacity
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-03-01 , DOI: 10.1109/tit.2019.2961919 Fatemeh Arbabjolfaei , Young-Han Kim
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-03-01 , DOI: 10.1109/tit.2019.2961919 Fatemeh Arbabjolfaei , Young-Han Kim
The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product structure in the side information graph is introduced as a natural condition under which the corresponding index coding problem can be decomposed into multiple interacting subproblems, each consisting of vertices with the same adjacency pattern with respect to other subproblems. For side information graphs with this structure, the capacity region is characterized in terms of the subproblem capacity regions combined in the same product structure. The proof is based on dual uses of random coding—one for a new multiletter characterization of the capacity region of a general index coding problem via joint typicality decoding and the other for a construction of a new multiletter code of matching rates from a single-letter code via joint typicality encoding. Several special cases are discussed that recover and strengthen known structural properties of the index coding capacity region.
中文翻译:
广义词典产品与索引编码能力
索引编码问题研究将多条消息广播到各自接收器的基本限制,这些消息具有由有向图表示的不同边信息集。引入边信息图中的广义词典产品结构作为自然条件,在该条件下,相应的索引编码问题可以分解为多个相互作用的子问题,每个子问题由相对于其他子问题具有相同邻接模式的顶点组成。对于具有这种结构的边信息图,容量区域的特征在于组合在同一产品结构中的子问题容量区域。该证明基于随机编码的双重用途——一个用于通过联合典型性解码对一般索引编码问题的容量区域进行新的多字母表征,另一个用于从单字母构建匹配率的新多字母代码通过联合典型性编码进行编码。讨论了恢复和加强索引编码容量区域的已知结构特性的几种特殊情况。
更新日期:2020-03-01
中文翻译:
广义词典产品与索引编码能力
索引编码问题研究将多条消息广播到各自接收器的基本限制,这些消息具有由有向图表示的不同边信息集。引入边信息图中的广义词典产品结构作为自然条件,在该条件下,相应的索引编码问题可以分解为多个相互作用的子问题,每个子问题由相对于其他子问题具有相同邻接模式的顶点组成。对于具有这种结构的边信息图,容量区域的特征在于组合在同一产品结构中的子问题容量区域。该证明基于随机编码的双重用途——一个用于通过联合典型性解码对一般索引编码问题的容量区域进行新的多字母表征,另一个用于从单字母构建匹配率的新多字母代码通过联合典型性编码进行编码。讨论了恢复和加强索引编码容量区域的已知结构特性的几种特殊情况。