Private Streaming with Convolutional Codes

TL;DR

This paper extends private information retrieval (PIR) schemes to streaming scenarios using convolutional codes, analyzing their properties and optimality under different server models, including Byzantine and colluding servers.

Contribution

It adapts the star product PIR scheme to streaming with convolutional codes and analyzes its properties and optimality for various server models.

Findings

Achieved PIR rates for streaming with convolutional codes.

Proved asymptotic optimality of the scheme for large file stripes.

Demonstrated the scheme's superiority over trivial stripe downloading in Byzantine models.

Abstract

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.