Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this paper, we study convertible codes, which enable the transformation of one code into another with minimum cost in the merge regime, addressing the latter. We derive general lower bounds on the read and write costs of linear code conversion, applicable to arbitrary linear codes. We then focus on Reed-Muller codes, which efficiently handle data heterogeneity, addressing the former issue, and construct explicit conversion procedures that, for the first time, combine both forms of heterogeneity for distributed data storage.

We investigate the problems of privately repairing erasures and evaluating their linear combinations for Reed-Solomon codes with low communication bandwidths. We propose two approaches: one based on hiding subspaces used to form parity-check equations, and another based on multiplying parity-check equations with random polynomials. We also derive a lower bound on the repair bandwidth for the single erasure case under reasonable assumptions about the schemes being used and demonstrate the optimality of the proposed schemes for codes of specific lengths.

Motivated by the use of trace codes in low-bandwidth repair, we investigate the decoding of a Reed-Solomon subcode whose information polynomials are characterized by a known sparse support. We ask: Can we correct more errors by leveraging the known structure of the information polynomial? We affirmatively respond to this query by introducing two schemes designed to complement any Reed-Solomon decoder. Our findings demonstrate better error-correcting capabilities than the naive way to decode based on the maximum degree of the information polynomial.

We investigate the problem of privately recovering a single erasure for Reed-Solomon codes with low communication bandwidths. For an$[n,k]_{\mathbb{F}_{q^{\ell}}}$code with$n-k\geq q^{m}+t-1$, we construct a repair scheme that allows a client to recover an arbitrary codeword symbol without leaking its index to any set of$t$colluding helper nodes at a repair bandwidth of$(n-1)(\ell-m)$sub-symbols in$\mathbb{F}_{q}$. When$t=1$, this reduces to the bandwidth of existing repair schemes based on subspace polynomials. We prove the optimality of the proposed scheme when$n=q^{\ell}$under a reasonable assumption about the schemes being used. Our private repair scheme can also be transformed into a private retrieval scheme for data encoded by Reed-Solomon codes.

We generalize the problem of recovering a lost/erased symbol in a Reed-Solomon code to the scenario in which some side information about the lost symbol is known. The side information is represented as a set$S$of linearly independent combinations of the sub-symbols of the lost symbol. When$S=\varnothing$, this reduces to the standard problem of repairing a single codeword symbol. When$S$is a set of sub-symbols of the erased one, this becomes the repair problem with partially lost/erased symbol. We first establish that the minimum repair bandwidth depends on$\vert S\vert$and not the content of$S$and construct a lower bound on the repair bandwidth of a linear repair scheme with side information$S$We then consider the well-known subspace-polynomial repair schemes and show that their repair bandwidths can be optimized by choosing the right subspaces. Finally, we demonstrate several parameter regimes where the optimal bandwidths can be achieved for full-length Reed-Solomon codes.

We consider the problem of evaluating distinct multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate polynomial is evaluated over its corresponding dataset and propose a generalization of the Lagrange Coded Computing framework (Yu et al., 2019) to perform all computations simultaneously while providing robustness against stragglers who do not respond in time, adversarial workers who respond with wrong computation and information-theoretic security of dataset against colluding workers. Our scheme introduces a small computation overhead which results in a reduction in download cost and also offers comparable resistance to stragglers over existing solutions. On top of it, we also propose two verification schemes to detect the presence of adversaries, which leads to incorrect results, without involving additional nodes.

Private Information Retrieval (PIR) protocols allow a client to retrieve any file of interest while keeping the files identity hidden from the database servers. While many existing PIR protocols assume servers to be honest but curious, we investigate the scenario of dishonest servers that provide incorrect answers to mislead clients into obtaining wrong results. We propose a unified framework for polynomial PIR protocols encompassing various existing protocols that optimize the download rate or total communication cost. We introduce a way to transform a polynomial PIR to a verifiable one without increasing the number of involved servers by doubling the queries. The security guarantees can be information-theoretic or computational, and the verification keys can be public or private. Moreover, in one of our protocols, the ratio between the additional download overhead associated with verification and the normal download cost approaches zero as the file size goes to infinity.

Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth schemes that evaluate the weighted sum of ℓ coded symbols in a codewordc∈ Fn, when we are given access todof the remaining components inc. Formally, suppose that F is a field extension of B of degreet. Letcbe a codeword in a Reed-Solomon code of dimensionkand our task is to compute the weighted sum of ℓ coded symbols. In this paper, for somest, we provide an explicit scheme that performs this task by downloadingd(t-s) sub-symbols in B fromdavailable nodes, wheneverd≥ ℓ|B|s-ℓ +k. In many cases, our scheme outperforms previous schemes in the literature. Furthermore, we provide a characterization of evaluation schemes for general linear codes. Then in the special case of Reed-Solomon codes, we use this characterization to derive a lower bound for the evaluation bandwidth.

Motivated by applications in distributed storage, distributed computing, and homomorphic secret sharing, we study communication-efficient schemes for computing linear combinations of coded symbols. Specifically, we design low-bandwidth schemes that evaluate the weighted sum of ℓ coded symbols in a codeword ${\mathbf{c}} \in {\mathbb{F}^n}$, when we are given access to d of the remaining components in c. Formally, suppose that $\mathbb{F}$ is a field extension of $\mathbb{B}$ of degree t. Let c be a codeword in a Reed-Solomon code of dimension k and our task is to compute the weighted sum of ℓ coded symbols. In this paper, for some s < t, we provide an explicit scheme that performs this task by downloading d(t − s) sub-symbols in $\mathbb{B}$ from d available nodes, whenever $d \geq \ell |\mathbb{B}{|^s} - \ell + k$. In many cases, our scheme outperforms previous schemes in the literature. Furthermore, we provide a characterization of evaluation schemes for general linear codes. Then in the special case of Reed-Solomon codes, we use this characterization to derive a lower bound for the evaluation bandwidth.

Private Information Retrieval (PIR) schemes allow a client to retrieve any file of interest, while hiding the file identity from the database servers. In contrast to most existing PIR schemes that assume honest-but-curious servers, we study the case of dishonest servers. The latter provide incorrect answers and try to persuade the client to output the wrong result. We introduce several PIR schemes with information-theoretic privacy and result verification for the case of two servers. Security guarantees can be information-theoretical or computational, and the verification keys can be public or private. In this work, our main performance metric is the download rate.

We consider the problem of designing a Private Information Retrieval (PIR) scheme on m files replicated on k servers that can collude or, even worse, can return incorrect answers. Our goal is to correctly retrieve a specific message while keeping its identity private from the database servers. We consider the asymptotic information-theoretic capacity of this problem defined as the maximum ratio of the number of correctly retrieved symbols to the downloaded one for a large enough number of stored files. We propose an achievable scheme with a small file size and prove that such a file size is minimal for the fixed number of retrieved symbols, solving the problem pointed out by Banawan and Ulukus.A full version [1] of this paper is accessible at: https://arxiv.org/abs/2302.02230

We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and investigate its code-distance properties. We propose three lower bounds on its minimum distance and study methods to efficiently correct errors close to these bounds.

We consider the problem of evaluating arbitrary multivariate polynomials over several massive datasets in a distributed computing system with a single master node and multiple worker nodes. We focus on the general case when each multivariate polynomial is evaluated over its dataset and propose a generalization of the Lagrange Coded Computing framework (Yu et al. 2019) to provide robustness against stragglers who do not respond in time, adversarial workers who respond with wrong computation and information-theoretic security of dataset against colluding workers. Our scheme introduces a small computation overhead which results in a reduction in download cost and also offers comparable resistance to stragglers over existing solutions.

A distributed storage system must support efficient access to stored data while ensuring recovery of temporally unavailable nodes. Another important aspect of a distributed storage system is security. In this paper, we bring these features together and investigate the problem of efficient access to stored data in presence of a passive eavesdropper with access to limited number of nodes. The access efficiency is measured in two different terms, namely, the number of accessed nodes and the volume of generated network traffic. These quantities possess a natural connection to locality and repair bandwidth in distributed storage system. For each of them we derive bounds on parameters and provide explicit constructions based on maximum distance separable codes. Motivated by practical perspectives we propose the techniques to ensure the same workload on each node as well as constructions over small fields based on subfield subcodes, Euclidean geometry codes and Reed-Muller codes. Finally, we derive an asymptotic random coding bound on parameters of a secure distributed storage system and propose further research directions.

A distributed storage system (DSS) needs to be efficiently accessible and repairable. Recently, considerable effort has been made towards the latter, while the former is usually not considered, since a trivial solution exists in the form of systematic encoding. However, this is not a viable option when considering storage that has to be secure against eavesdroppers. This work investigates the problem of efficient access to data stored on a DSS under such security constraints. Further, we establish methods to balance the access load, i.e., ensure that each node is accessed equally often. We establish the capacity for the alphabet independent case and give an explicit code construction. For the alphabet-dependent case we give existence results based on a random coding argument.

Due to the constant growth of the total amount of data stored by humanity the interest in distributed storage systems significantly increases. Recently considerable effort has been made toward efficient access to stored data and repair of temporally unavailable nodes while security issues are kept outside the mainstream of research. In this paper, we present different eavesdropper models for distributed storage tasks as well as possible extensions of distributed storage frameworks to secure against them. This is ongoing research in the framework of Ph.D. study at Skolkovo Institute of Science and Technology under the supervision of Alexey Frolov and Grigory Kabatiansky started in November 2017 and tentative end date in November 2021.

Blockchain-based solutions can significantly decrease potential losses from counterfeit products in the majority of existing supply chains. In this paper, we present an architecture of a supply-chain management solution for the plastic pipes market and demonstrate its' feasibility of industrial scenarios. We emulate such a system for plastic pipes factory based on the Exonum blockchain framework and show the robustness and reliability of the proposed system.

In this paper we propose a new low power resource management for Low Earth Orbit (LEO) satellite communication system with a hybrid multi-beamforming. LEO satellite communication systems are known to have a serious mobility management problem, resulting in inefficient radio resources management and extra power consumption. Joint time/frequency/space resources allocation requires a lot of computational resources to serve thousands of active users. Data traffic suffers from a huge amount of service data, caused by multiple time-frequency resources reallocation. The Earth’s footprint has a curved ellipse shape, which also requires extra computations to calculate the user time location inside a single beam. By utilizing hybrid beamforming structure of the system, we propose a low power resource allocation scheme with a minimal control channel traffic.

Blockchain technology has a lot of applications including but not limited to cryptotokens. For example, permissioned blockchains for state registries can include no money logic inside. But the creation of cryptotoken is a typical example of blockchain application and is a popular model to measure performance. In this paper, we described how to construct an account-based cryptotoken using Exonum, an open-source framework for creating blockchain applications, and by the means of performance tests shown that the proposed solution meets real-life throughput requirements for many applications. The proposed approach can be used to create cryptocurrencies in other open-source frameworks focused on permissioned blockchain applications.

In this paper, we extend the notion of locally recoverable codes with availability to secret sharing schemes. The main problem that we considered is how to store information using locally recoverable codes with all symbol locality and availability in such way that useful information can be recovered using an only small subset of coordinates while a user who observes less than a certain number of coordinates does not get any information. In other words, we have to protect locally recoverable codes with availability over passive eavesdropper that can observe only limited number of coordinates. Upper bounds on number of bits that can be securely stored in such systems together with explicit constructions of codes with such a property are proposed.

We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the shortening method and generalized Hamming weights that are fundamental parameters of any linear codes with many useful applications. This bound improves existing upper bounds. To reduce the gap in between upper and lower bounds, we do not restrict the alphabet size and propose explicit constructions of codes with locality and availability via rank-metric codes. The first construction relies on expander graphs and is better in low rate region. The second construction utilizes the LRC codes developed by Wang et al. as inner codes and is better in high rate region. We also suggest one possible generalization of LRC codes in which the recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. We derive upper and lower bounds on the parameters of such codes and present explicit constructions of codes with such a property.

We continue our investigation of one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive upper and lower bounds on the minimum distance of such codes. The upper bound is based on generalized Hamming weights (GHWs) that are fundamental parameters of any linear codes with many useful applications. In order to derive a lower bound we propose an explicit construction of (r, t, x), -LRC via rank-metric codes and previously developed high rate (r, t, x) -LRC codes.

In this paper a cloud version of distributed reception scenario is analyzed in automated parking system. A parking sensor has a single antenna transmitter sending data to a large number of geographically separated single antenna receive routers. This scenario is applicable in smart parking system (SPS) enabled by Internet of Things (IoT). We propose a new functional split, which enables multiple-input multiple-output (MIMO) detection in cloud server and non-binary low density parity check (LDPC) codes application in SPS. The proposed architecture is intended to increase the uplink performance significantly in shadowed scenario and in strong interference scenario, leading to significant battery power saving in IoT sensor. Among other things, such approach requires less expenses due to reduced routers complexity and fits in future 5G concepts of massive IoT.

We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the shortening method and improves existing shortening bounds. To reduce the gap in between upper and lower bounds we do not restrict the alphabet size and propose explicit constructions of codes with locality and availability via rank-metric codes. The first construction relies on expander graphs and is better in low rate region, the second construction utilizes LRC codes developed by Wang et al. as inner codes and better in high rate region.

We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive an upper bound for the rate of such codes and give explicit constructions of codes with such a property. These constructions utilize LRC codes developed by Wang et al.