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首页> 外文会议>IEEE International Symposium on Information Theory >Symmetric Private Information Retrieval with Mismatched Coded Messages and Randomness
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Symmetric Private Information Retrieval with Mismatched Coded Messages and Randomness

机译：具有不匹配的编码消息和随机性的对称私人信息检索

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The capacity of symmetric private information retrieval (PIR) with N servers and K messages, each coded by an (N, M)-MDS code has been characterized as ${C_{{ext{MDS - SPIR}}}} = 1 - rac{M}{N}$. A critical assumption for this result is that the randomness is similarly coded by an (N, M)-MDS code, i.e., the code parameters of the messages and randomness are matched. In this work, we are interested in the mismatched case, and as a preliminary result, we establish the capacity of the mismatched MDS coded symmetric PIR (SPIR) problem under an extreme setting, where the messages are coded by an (N, M)-MDS code and the randomness is replicated (i.e., coded by an (N, 1)-MDS code). The capacity is shown to be ${C_{{ext{mis}} - {ext{MDS}} - {ext{SPIR}}}} = left( {1 - rac{1}{N}} ight) cdot {left( {1 + rac{{M - 1}}{N}left( {1 + rac{M}{N} + cdots + {{left( {rac{M}{N}} ight)}^{K - 2}}} ight)} ight)^{ - 1}}$. Interestingly, Cmis-MDS-SPIR > CMDS-SPIR, so mismatched coded randomness (with more redundancy) is strictly beneficial. Further, mismatched SPIR exhibits properties that are similar to PIR.
机译：具有N个服务器和K条消息（每个都由（N，M）-MDS代码编码）的对称私有信息检索（PIR）的容量已表征为$ {C _ {{\ text {MDS-SPIR}}}}} = 1 -\ frac {M} {N} $。对于该结果的关键假设是，随机性类似地由（N，M）-MDS代码编码，即，消息的代码参数和随机性被匹配。在这项工作中，我们对不匹配的情况感兴趣，作为初步结果，我们建立了在极端设置下消息不匹配的MDS编码对称PIR（SPIR）问题的容量，其中消息由（N，M）编码-MDS代码和随机性被复制（即，由（N，1）-MDS代码编码）。容量显示为$ {C _ {{\ text {mis}}-{\ text {MDS}}-{\ text {SPIR}}}} = \ left（{1-\ frac {1} {N} } \ right）\ cdot {\ left（{1 + \ frac {{M-1}}} {N} \ left（{1 + \ frac {M} {N} + \ cdots + {{\ left（{\ frac {M} {N}} \ right）} ^ {K-2}}} \ right）} \ right）^ {-1}} $。有趣的是，C mis-MDS-SPIR > C MDS-SPIR ，因此不匹配的编码随机性（具有更大的冗余度）绝对是有利的。此外，不匹配的SPIR表现出与PIR相似的特性。

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