Recently, information-theoretic private information retrieval (PIR) from coded storage systems has gained a lot of attention, and a general star product PIR scheme was proposed. In this paper, the star product scheme is adopted, with appropriate modifications, to the case of private (e.g., video) streaming. It is assumed that the files to be streamed are stored on $n$ servers in a coded form, and the streaming is carried out via a convolutional code. The star product scheme is defined for this special case, and various properties are analyzed for two channel models related to straggling and Byzantine servers, both in the baseline case as well as with colluding servers. The achieved PIR rates for the given models are derived and, for the cases where the capacity is known, the first model is shown to be asymptotically optimal, when the number of stripes in a file is large. The second scheme introduced in this work is shown to be the equivalent of block convolutional codes in the PIR setting. For the Byzantine server model, it is shown to outperform the trivial scheme of downloading stripes of the desired file separately without memory.

中文翻译：

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带有卷积码的私人流媒体

最近，来自编码存储系统的信息论私人信息检索（PIR）引起了很多关注，并提出了通用的明星产品PIR方案。在本文中，采用明星产品方案，并适当修改，用于私人（例如，视频）流的情况。假设要流式传输的文件以编码形式存储在 $n$ 个服务器上，并且流式传输是通过卷积码进行的。针对这种特殊情况定义了明星产品方案，并分析了与散列服务器和拜占庭服务器相关的两个通道模型的各种属性，无论是在基线情况下还是与共谋服务器。推导出给定模型实现的 PIR 率，对于已知容量的情况，第一个模型显示为渐近最优，当文件中的条带数量很大时。在这项工作中引入的第二种方案被证明与 PIR 设置中的块卷积码等效。对于拜占庭服务器模型，它表现出优于无需内存的情况下单独下载所需文件的条带的简单方案。