200 research outputs found
Secure Repairable Fountain Codes
In this letter, we provide the construction of repairable fountain codes
(RFCs) for distributed storage systems that are information-theoretically
secure against an eavesdropper that has access to the data stored in a subset
of the storage nodes and the data downloaded to repair an additional subset of
storage nodes. The security is achieved by adding random symbols to the
message, which is then encoded by the concatenation of a Gabidulin code and an
RFC. We compare the achievable code rates of the proposed codes with those of
secure minimum storage regenerating codes and secure locally repairable codes.Comment: To appear in IEEE Communications Letter
Secure and Private Cloud Storage Systems with Random Linear Fountain Codes
An information theoretic approach to security and privacy called Secure And
Private Information Retrieval (SAPIR) is introduced. SAPIR is applied to
distributed data storage systems. In this approach, random combinations of all
contents are stored across the network. Our coding approach is based on Random
Linear Fountain (RLF) codes. To retrieve a content, a group of servers
collaborate with each other to form a Reconstruction Group (RG). SAPIR achieves
asymptotic perfect secrecy if at least one of the servers within an RG is not
compromised. Further, a Private Information Retrieval (PIR) scheme based on
random queries is proposed. The PIR approach ensures the users privately
download their desired contents without the servers knowing about the requested
contents indices. The proposed scheme is adaptive and can provide privacy
against a significant number of colluding servers.Comment: 8 pages, 2 figure
Locality and Availability in Distributed Storage
This paper studies the problem of code symbol availability: a code symbol is
said to have -availability if it can be reconstructed from disjoint
groups of other symbols, each of size at most . For example, -replication
supports -availability as each symbol can be read from its other
(disjoint) replicas, i.e., . However, the rate of replication must vanish
like as the availability increases.
This paper shows that it is possible to construct codes that can support a
scaling number of parallel reads while keeping the rate to be an arbitrarily
high constant. It further shows that this is possible with the minimum distance
arbitrarily close to the Singleton bound. This paper also presents a bound
demonstrating a trade-off between minimum distance, availability and locality.
Our codes match the aforementioned bound and their construction relies on
combinatorial objects called resolvable designs.
From a practical standpoint, our codes seem useful for distributed storage
applications involving hot data, i.e., the information which is frequently
accessed by multiple processes in parallel.Comment: Submitted to ISIT 201
Update-Efficiency and Local Repairability Limits for Capacity Approaching Codes
Motivated by distributed storage applications, we investigate the degree to
which capacity achieving encodings can be efficiently updated when a single
information bit changes, and the degree to which such encodings can be
efficiently (i.e., locally) repaired when single encoded bit is lost.
Specifically, we first develop conditions under which optimum
error-correction and update-efficiency are possible, and establish that the
number of encoded bits that must change in response to a change in a single
information bit must scale logarithmically in the block-length of the code if
we are to achieve any nontrivial rate with vanishing probability of error over
the binary erasure or binary symmetric channels. Moreover, we show there exist
capacity-achieving codes with this scaling.
With respect to local repairability, we develop tight upper and lower bounds
on the number of remaining encoded bits that are needed to recover a single
lost bit of the encoding. In particular, we show that if the code-rate is
less than the capacity, then for optimal codes, the maximum number
of codeword symbols required to recover one lost symbol must scale as
.
Several variations on---and extensions of---these results are also developed.Comment: Accepted to appear in JSA
Locally Repairable Convolutional Codes With Sliding Window Repair
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, ∂−1 erasures per local group), and sliding-window global repair, which can correct erasure patterns with up to dcj−1 erasures in every window of j+1 consecutive blocks of n nodes, where dcj−1 is the j th column distance of the code. The parameter j can be adjusted, for a fixed LRCC, according to different catastrophic erasure patterns, requiring only to contact n(j+1)−dcj+1 nodes, plus less than μn other nodes, in the storage system, where μ is the memory of the code. A Singleton-type bound is provided for dcj−1 . If it attains such a bound, an LRCC can correct the same number of catastrophic erasures in a window of length n(j+1) as an optimal locally repairable block code of the same rate and locality, and with block length n(j+1) . In addition, the LRCC is able to perform the flexible and somehow local sliding-window repair by adjusting j . Furthermore, by adjusting and/or sliding the window, the LRCC can potentially correct more erasures in the original window of n(j+1) nodes than an optimal locally repairable block code of the same rate and locality, and length n(j+1) . Finally, the concept of partial maximum distance profile (partial MDP) codes is introduced. Partial MDP codes can correct all information-theoretically correctable erasure patterns for a given locality, local distance and information rate. An explicit construction of partial MDP codes whose column distances attain the provided Singleton-type bound, up to certain parameter j=L , is obtained based on known maximum sum-rank distance convolutional codes.This work was supported in part by the Independent Research Fund Denmark under Grant DFF-7027-00053B, in part by the Generalitat Valenciana under Grant AICO/2017/128, and in part by the Universitat d’Alacant under Grant VIGROB-287
- …