A general private information retrieval scheme for MDS coded databases with colluding servers

TL;DR

This paper proposes a new private information retrieval scheme for MDS coded databases with colluding servers, achieving higher rates than existing schemes for certain parameters, applicable to any MDS code in distributed storage.

Contribution

It introduces a general PIR scheme for MDS coded databases with colluding servers that improves retrieval rate performance over existing methods.

Findings

Achieves rate $(1+R+R^2+\cdots+R^{M-1})$ with $R=1-\frac{{{N-T}\choose K}}{{N\choose K}}$

Performs better than existing schemes for specific parameter ranges

Applicable to any underlying MDS code in distributed storage systems

Abstract

The problem of private information retrieval gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. PIR capacity is the maximal number of bits privately retrieved per one bit of downloaded bit. The capacity has been fully solved for some degenerating cases. For a general case where the database is both coded and colluded, the exact capacity remains unknown. We build a general private information retrieval scheme for MDS coded databases with colluding servers. Our scheme achieves the rate $(1+R+R^2+\cdots+R^{M-1})$, where $R=1-\frac{{{N-T}\choose K}}{{N\choose K}}$. Compared to existing PIR schemes, our scheme performs better for a certain range of parameters and is suitable for any underlying MDS code used in the distributed storage system.