On critical index coding problems

Fatemeh Arbabjolfaei, Young-Han Kim
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引用次数: 8

Abstract

The question of under what condition some side information for index coding can be removed without affecting the capacity region is studied, which was originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question, the notion of unicycle for the side information graph is introduced and it is shown that any edge that belongs to a unicycle is critical, namely, it cannot be removed without reducing the capacity region. Although this sufficient condition for criticality is not necessary in general, a partial converse is established, which elucidates the connection between the notion of unicycle and the maximal acylic induced subgraph outer bound on the capacity region by Bar-Yossef, Birk, Jayram, and Kol.
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关键索引编码问题
研究了在什么条件下可以在不影响容量区域的情况下删除索引编码的一些侧信息的问题,这个问题最初是由Tahmasbi、Shahrasbi和Gohari提出的。为了回答这个问题,引入了边信息图的独轮车的概念,并证明了任何属于独轮车的边都是关键的,即在不减小容量区域的情况下,它不能被移除。虽然这个临界性的充分条件在一般情况下不是必需的,但是Bar-Yossef、Birk、Jayram和Kol建立了一个部分逆,说明了单环的概念与容量区域上的最大无环诱导子图外界之间的联系。
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