安全分散柔性索引编码
Secure Decentralized Pliable Index Coding
摘要：
本文研究柔韧指数编码（PICOD）问题的一种变体，即，索引编码问题，其中用户可以通过解码不在其边信息集中的任何消息来满足，其中通信是分散的，即，它发生在用户之间而不是由中央服务器进行，并且是安全的，即，每个用户仅被允许解码其辅助信息集之外的一个消息，并且必须不能收集关于不是其解码的消息的任何其它消息的任何信息。鉴于这个问题的一般版本的困难，本文侧重于的情况下，边信息集是“$s$ ~循环移位”，即，用户$u$的边信息集是由$\{u, u+1, \ldots, u+s-1\}$为一些固定的$s$和其中的索引打算模的消息集的基数索引的消息集。在“分散式非安全”和“集中式安全”设置中研究了这一特定设置，从而可以在传输次数的安全限制下量化分散式通信的成本。有趣的是，去中心化与集中式安全设置之间的差距约为3。这与没有安全约束的情况相反，在没有安全约束的情况下，已知乘法间隙至多为2。
英文摘要：
This paper studies a variant of the Pliable Index CODing (PICOD) problem, i.e., an index coding problem where a user can be satisfied by decoding any message that is not in its side information set, where communication is decentralized, i.e., it occurs among users rather than by the central server, and secure, i.e., each user is allowed to decode only one message outside its side information set and must not be able to collect any information about any other message that is not its decoded one. Given the difficulty of the general version of this problem, this paper focuses on the case where the side information sets are `$s$~circular shifts', namely, user $u$'s side information set is the set of messages indexed by $\{u, u+1, \ldots, u+s-1\}$ for some fixed $s$ and where the indices are intended modulo the cardinality of the message set. This particular setting has been studied in the `decentralized non-secure' and in the `centralized secure' settings, thus allows one to quantify the cost of decentralized communication under security constraints on the number of transmissions. Interestingly, the decentralized vs the centralized secure setting incurs a multiplicative gap of approximately~three. This is in contrast to the cases without security constraint, where the multiplicative gap is known to be at most two.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
