1,084 research outputs found
Private Information Retrieval Schemes With Product-Matrix MBR Codes
A private information retrieval (PIR) scheme allows a user to retrieve a file from a database without revealing any information on the file being requested. As of now, PIR schemes have been proposed for several kinds of storage systems, including replicated and MDS-coded systems. However, the problem of constructing PIR schemes on regenerating codes has been sparsely considered. A regenerating code is a storage code whose codewords are distributed among nodes, enabling efficient storage of files, as well as low-bandwidth retrieval of files and repair of nodes. Minimum-bandwidth regenerating (MBR) codes define a family of regenerating codes allowing a node repair with optimal bandwidth. Rashmi, Shah, and Kumar obtained a large family of MBR codes using the product-matrix (PM) construction. In this work, a new PIR scheme over PM-MBR codes is designed. The inherent redundancy of the PM structure is used to reduce the download communication complexity of the scheme. A lower bound on the PIR capacity of MBR-coded PIR schemes is derived, showing an interesting storage space vs. PIR rate trade-off compared to existing PIR schemes with the same reconstruction capability. The present scheme also outperforms a recent PM-MBR PIR construction of Dorkson and Ng.Peer reviewe
Storage Codes with Flexible Number of Nodes
This paper presents flexible storage codes, a class of error-correcting codes
that can recover information from a flexible number of storage nodes. As a
result, one can make a better use of the available storage nodes in the
presence of unpredictable node failures and reduce the data access latency. Let
us assume a storage system encodes information symbols over a finite
field into nodes, each of size symbols. The code is
parameterized by a set of tuples ,
satisfying and , such that the information symbols can be reconstructed from any
nodes, each node accessing symbols. In other words, the code
allows a flexible number of nodes for decoding to accommodate the variance in
the data access time of the nodes. Code constructions are presented for
different storage scenarios, including LRC (locally recoverable) codes, PMDS
(partial MDS) codes, and MSR (minimum storage regenerating) codes. We analyze
the latency of accessing information and perform simulations on Amazon clusters
to show the efficiency of presented codes
Private Streaming with Convolutional Codes
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~ 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
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