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Register a new userPractical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes
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Added by
Nitish Mital
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The nodes are connected wirelessly, hence all transmissions by helper nodes during a repair round are available to all the nodes being repaired. The scheme is simple and practical because of low subpacketization, low I/O cost and low computational cost. Achievability of the minimum-bandwidth regenerating (MBR) point, as well as an interior point, on the optimal storage-repair bandwidth tradeoff curve is shown. The subspace properties derived in the paper provide insight into the general properties of functional regenerating codes.
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The problem of exact-repair regenerating codes against eavesdropping attack is studied. The eavesdropping model we consider is that the eavesdropper has the capability to observe the data involved in the repair of a subset of $ell$ nodes. An $(n,k,d,ell)$ secure exact-repair regenerating code is an $(n,k,d)$ exact-repair regenerating code that is secure under this eavesdropping model. It has been shown that for some parameters $(n,k,d,ell)$, the associated optimal storage-bandwidth tradeoff curve, which has one corner point, can be determined. The focus of this paper is on characterizing such parameters. We establish a lower bound $hat{ell}$ on the number of wiretap nodes, and show that this bound is tight for the case $k = d = n-1$.
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcast constraints. The polarization-based codes achieve rates on the boundary of the private-message capacity region. For two-user noisy broadcast channels, polar implementations are presented for two information-theoretic schemes: i) Covers superposition codes; ii) Martons codes. Due to the structure of polarization, constraints on the auxiliary and channel-input distributions are identified to ensure proper alignment of polarization indices in the multi-user setting. The codes achieve rates on the capacity boundary of a few classes of broadcast channels (e.g., binary-input stochastically degraded). The complexity of encoding and decoding is $O(n*log n)$ where $n$ is the block length. In addition, polar code sequences obtain a stretched-exponential decay of $O(2^{-n^{beta}})$ of the average block error probability where $0 < beta < 0.5$.
This short note revisits the problem of designing secure minimum storage regenerating (MSR) codes for distributed storage systems. A secure MSR code ensures that a distributed storage system does not reveal the stored information to a passive eavesdropper. The eavesdropper is assumed to have access to the content stored on $ell_1$ number of storage nodes in the system and the data downloaded during the bandwidth efficient repair of an additional $ell_2$ number of storage nodes. This note combines the Gabidulin codes based precoding [18] and a new construction of MSR codes (without security requirements) by Ye and Barg [27] in order to obtain secure MSR codes. Such optimal secure MSR codes were previously known in the setting where the eavesdropper was only allowed to observe the repair of $ell_2$ nodes among a specific subset of $k$ nodes [7, 18]. The secure coding scheme presented in this note allows the eavesdropper to observe repair of any $ell_2$ ouf of $n$ nodes in the system and characterizes the secrecy capacity of linear repairable MSR codes.
In this paper, we revisit the problem of finding the longest systematic-length $k$ for a linear minimum storage regenerating (MSR) code with optimal repair of only systematic part, for a given per-node storage capacity $l$ and an arbitrary number of parity nodes $r$. We study the problem by following a geometric analysis of linear subspaces and operators. First, a simple quadratic bound is given, which implies that $k=r+2$ is the largest number of systematic nodes in the emph{scalar} scenario. Second, an $r$-based-log bound is derived, which is superior to the upper bound on log-base $2$ in the prior work. Finally, an explicit upper bound depending on the value of $frac{r^2}{l}$ is introduced, which further extends the corresponding result in the literature.
High availability of containerized applications requires to perform robust storage of applications state. Since basic replication techniques are extremely costly at scale, storage space requirements can be reduced by means of erasure or repairing codes. In this paper we address storage regeneration using repair codes, a robust distributed storage technique with no need to fully restore the whole state in case of failure. In fact, only the lost servers content is replaced. To do so, new cleanslate storage units are made operational at a cost for activating new storage servers and a cost for the transfer of repair data. Our goal is to guarantee maximal availability of containers state files by a given deadline. activation of servers and communication cost. Upon a fault occurring at a subset of the storage servers, we aim at ensuring that they are repaired by a given deadline. We introduce a controlled fluid model and derive the optimal activation policy to replace servers under such correlated faults. The solution concept is the optimal control of regeneration via the Pontryagin minimum principle. We characterise feasibility conditions and we prove that the optimal policy is of threshold type. Numerical results describe how to apply the model for system dimensioning and show the tradeoff between
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