Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for both unique string reconstruction and correction of multiple mass errors. We consider two approaches: The first approach pertains to asymmetric errors and it is based on introducing redundancy that scales linearly with the number of errors and logarithmically with the length of the string. The construction allows for the string to be uniquely reconstructed based only on its erroneous substring composition multiset. The key idea behind our unique reconstruction approach is to interleave (shifted) Catalan-Bertrand paths with arbitrary binary strings and "reflect" them so as to force prefixes and suffixes of the same length to have different weights. The asymptotic code rate of the scheme is one, and decoding is accomplished via a simplified version of the backtracking algorithm used for the Turnpike problem. For symmetric errors, we use a polynomial characterization of the mass information and adapt polynomial evaluation code constructions for this setting. In the process, we develop new efficient decoding algorithms for a constant number of composition errors and show that the redundancy of the scheme scales quadratically with the number of errors and logarithmically with the codelength.
Index coding is often studied with the assumption that a single source has all the messages requested by the receivers. We refer to this as \emph{centralized} index coding. In contrast, this paper focuses on \emph{distributed} index coding and addresses the following question: How does the availability of messages at distributed sources (storage nodes) affect the solutions and achievable rates of index coding? An extension to the work of Arbabjolfaei et al. in ISIT 2013 is presented when distributed sources communicate via a semi-deterministic multiple access channel (MAC) to simultaneous rece…
In this paper, we introduce a model of a single-failure locally recoverable distributed storage system. This model appears to give rise to a problem seemingly dual of the well-studied index coding problem. The relation between the dimensions of an optimal index code and optimal distributed storage code of our model has been established in this paper. We also show some extensions to vector codes.
In this paper we define the overflow problem of a network coding storage system in which the encoding parameter and the storage parameter are mismatched. Through analyses and experiments, we first show the impacts of the overflow problem in a network coding scheme, which not only waste storage spaces, but also degrade coding efficiency. To avoid the overflow problem, we then develop the network coding based secure storage (NCSS) scheme. Thanks to considering both security and storage requirements in encoding procedures and distributed architectures, the NCSS can improve the performance of a cl…
In the emerging field of DNA storage, data is encoded as DNA sequences and stored. The data is read out again by sequencing the stored DNA. Nanopore sequencing is a new sequencing technology that has many advantages over other methods; in particular, it is cheap, portable, and can support longer reads. While several practical coding schemes have been developed for DNA storage with nanopore sequencing, the theory is not well understood. Towards that end, we study a highly abstracted (deterministic) version of the nanopore sequencer, which highlights key features that make its analysis difficult…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol insertion/deletion, and limited-magnitude errors in symbols. Various parameter regimes are studied. New bounds on code parameters are provided, which improve upon known bounds. New codes are constructed, at times matching the bounds up to lower-or der terms or small constant factors.
In applications of distributed storage systems to distributed computing and implementation of key- value stores, the following property, usually referred to as consistency in computer science and engineering, is an important requirement: as the data stored changes, the latest version of the data must be accessible to a client that connects to the storage system. An information theoretic formulation called multi-version coding is introduced in the paper, in order to study storage costs of consistent distributed storage systems. Multi-version coding is characterized by ν totally ordered versions…
Motivated by polymer-based data-storage platforms that use chains of binary synthetic polymers as the recording media and read the content via tandem mass spectrometers, we propose a new family of codes that allows for unique string reconstruction and correction of one mass error. Our approach is based on introducing redundancy that scales logarithmically with the length of the string and allows for the string to be uniquely reconstructed based only on its erroneous substring composition multiset. The key idea behind our unique reconstruction approach is to interleave Catalan-type paths with a…
Due to the redundant nature of DNA synthesis and sequencing technologies, a basic model for a DNA storage system is a multi-draw "shuffling-sampling" channel. In this model, a random number of noisy copies of each sequence is observed at the channel output. Recent works have characterized the capacity of such a DNA storage channel under different noise and sequencing models, relying on sophisticated typicality-based approaches for the achievability. Here, we consider a multi-draw DNA storage channel in the setting of noise corruption by a binary erasure channel. We show that, in this setting, …
In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors within that model are losses of whole sequences and point errors inside the sequences, such as substitutions, insertions and deletions. We propose code constructions which can correct these errors with efficient encoders and decoders. By deriving upper bounds on the cardinalities of these codes using sphere packing arguments, we show that many of our codes are cl…
Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage efficiency. At the same time, in such large scale distributed storage systems, nodes fail on a regular basis, and the contents stored on them need to be regenerated and stored on other healthy nodes, the efficiency of which is an important factor affecting the overall quality of service. In this work, we formulate the problem of multilevel diversity coding with regene…
From currency to cloud storage systems, the continuous rise of the blockchain technology is moving various information systems towards decentralization. Blockchain-based decentralized storage networks (DSNs) offer significantly higher privacy and lower costs to customers compared with centralized cloud storage associated with specific vendors. Coding is required in order to retrieve data stored on failing components. While coding solutions for centralized storage have been intensely studied, topology-aware coding for heterogeneous DSNs have not yet been discussed. In this paper, we propose a j…
Three science and engineering problems of recent interests -index coding, locally recoverable distributed storage, and guessing games on graphs- are discussed and the connection between their optimal solutions is elucidated. By generalizing recent results by Shanmugam and Dimakis and by Mazumdar on the complementarity between the optimal broadcast rate of an index coding problem on a directed graph and the normalized rate of a locally recoverable distributed storage problem on the same graph, it is shown that the capacity region and the optimal rate region of these two problems are complementa…
In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors within that model are a loss of whole sequences and point errors inside the sequences, such as insertions, deletions and substitutions. We derive Gilbert-Varshamov lower bounds and sphere packing upper bounds on achievable cardinalities of error-correcting codes within this storage model. We further propose explicit code constructions than can correct errors…
Motivated by applications in distributed storage, the storage capacity of a graph was recently defined to be the maximum amount of information that can be stored across the vertices of a graph such that the information at any vertex can be recovered from the information stored at the neighboring vertices. Computing the storage capacity is a fundamental problem in network coding and is related, or equivalent, to some well-studied problems such as index coding with side information and generalized guessing games. In this paper, we consider storage capacity as a natural information-theoretic anal…
The {\em repair locality} of a distributed storage code is the maximum number of nodes that ever needs to be contacted during the repair of a failed node. Having small repair locality is desirable, since it is proportional to the number of disk accesses during repair. However, recent publications show that small repair locality comes with a penalty in terms of code distance or storage overhead if exact repair is required. Here, we first review some of the main results on storage codes under various repair regimes and discuss the recent work on possible (information-theoretical) trade-offs betw…
In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. The recent rise of the blockchain technology is also moving various information systems towards decentralization to achieve high privacy at low costs. While codes with hierarchical locality have been intensively studied in the context of centralized cloud storage due to their effectiveness in reducing the average reading time, those for decentral…
We consider the problem of storing data in a distributed manner over $T$ servers. We require the data (i) to be recoverable from the $T$ servers, and (ii) to remain private from any $T-1$ colluding servers, where privacy is quantified in terms of mutual information between the data and all the information available at the $T-1$ colluding servers. For this model, we determine (i) the fundamental trade-off between storage size and the level of desired privacy, (ii) the optimal amount of local randomness necessary at the encoder, and (iii)~an explicit low-complexity coding scheme that solely reli…
A method for encoding information in DNA sequences is described. The method is based on the precision-resolution framework, and is aimed to work in conjunction with a recently suggested terminator-free template independent DNA synthesis method. The suggested method optimizes the amount of information bits per synthesis time unit, namely, the writing rate. Additionally, the encoding scheme studied here takes into account the existence of multiple copies of the DNA sequence, which are independently distorted. Finally, quantizers for various run-length distributions are designed.
In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. Codes with hierarchical locality have been intensively studied due to their effectiveness in reducing the average reading time in cloud storage. In this paper, we present the first codes with hierarchical locality that achieve scalability and flexibility in heterogeneous cloud storage using small field size. We propose a double-level construction…
In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node. Efficient repair calls for erasure codes that in the face of node failure, are efficient in terms of minimizing the amount of repair data transferred over the network, the amount of data accessed at a helper node as well as the number of helper nodes contacted. Coding theory has evolved to handle these challenges by introducing two new classes of erasure codes,…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes for DNA storage channel, a new metric, termed the sequence-subset distance, is introduced, which generalizes the Hamming distance to a distance function defined between any two sets of unordered vectors and helps to establish a uniform framework to design error correcting codes for DNA storage channel. We further introduce a family of error correcting codes,…
Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of…
The problem of multilevel diversity coding with secure regeneration is revisited. Under the assumption that the eavesdropper can access the repair data for all compromised storage nodes, Shao el al. provided a precise characterization of the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff region. In this paper, it is shown that the MBR point of the achievable normalized storage-capacity repair-bandwidth tradeoff region remains the same even if we assume that the eavesdropper can access the repair data for some compromised stora…
We consider the problem of correcting mass readout errors in information encoded in binary polymer strings. Our work builds on results for string reconstruction problems using composition multisets [Acharya et al., 2015] and the unique string reconstruction framework proposed in [Pattabiraman et al., 2019]. Binary polymer-based data storage systems [Laure et al., 2016] operate by designing two molecules of significantly different masses to represent the symbols $\{0,1\}$ and perform readouts through noisy tandem mass spectrometry. Tandem mass spectrometers fragment the strings to be read into …
A network coding-based scheme is proposed to improve the energy efficiency of distributed storage systems in WSNs (wireless sensor networks), which mainly focuses on two problems: firstly, consideration is given to effective distributed storage technology in WSNs; secondly, we address how to repair the data in failed storage nodes with less resource. For the first problem, we propose a method to obtain a sparse generator matrix to construct network codes, and this sparse generator matrix is proven to be the sparsest. Benefiting from the sparse generator matrix, the energy consumption required …
Flash memory is a non-volatile computer memory comprised of blocks of cells, wherein each cell is implemented as either NAND or NOR floating gate. NAND flash is currently the most widely used type of flash memory. In a NAND flash memory, every block of cells consists of numerous pages; rewriting even a single page requires the whole block to be erased and reprogrammed. Block erasures determine both the longevity and the efficiency of a flash memory. Therefore, when data in a NAND flash memory are reorganized, minimizing the total number of block erasures required to achieve the desired data mo…
The amount of digital data is rapidly growing. There is an increasing use of a wide range of computer systems, from mobile devices to large-scale data centers, and important for reliable operation of all computer systems is mitigating the occurrence and the impact of errors in digital data. The demand for new ultra-fast and highly reliable coding techniques for data at rest and for data in transit is a major research challenge. Reliability is one of the most important design requirements. The simplest way of providing a degree of reliability is by using data replication techniques. However, re…
The exponential growth in data generation and large-scale data analysis creates an unprecedented need for inexpensive, low-latency, and high-density information storage. This need has motivated significant research into multi-level memory systems that can store multiple bits of information per device. Although both the memory state of these devices and much of the data they store are intrinsically analog-valued, both are quantized for use with digital systems and discrete error correcting codes. Using phase change memory as a prototypical multi-level storage technology, we herein demonstrate t…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous and efficient protocol should be used to repair the failed node. The repair process causes traffic and consequently transmission cost in the network. Recent results found the optimal trafficstorage tradeoff, and proposed regenerating codes to achieve the optimality. We aim at minimizing the transmission cost in the repair process. We consider the network to…
Many storage channels admit reading and rewriting of the content at a given cost. We consider rewritable channels with a hidden state which models the unknown characteristics of the memory cell. In addition to mitigating the effect of the write noise, rewrites can help the write controller obtain a better estimate of the hidden state. The paper has two contributions. The first is a lower bound on the capacity of a general rewritable channel with hidden state. The lower bound is obtained using a coding scheme that combines Gelfand-Pinsker coding with superposition coding. The rewritable AWGN ch…
Motivated by applications in distributed storage and distributed computation, we introduce embedded index coding (EIC). EIC is a type of distributed index coding in which nodes in a distributed system act as both senders and receivers of information. We show how embedded index coding is related to index coding in general, and give characterizations and bounds on the communication costs of optimal embedded index codes. We also define task-based EIC, in which each sending node encodes and sends data blocks independently of the other nodes. Task-based EIC is more computationally tractable and has…
The capacity of private information retrieval (PIR) from databases coded using maximum distance separable (MDS) codes has been previously characterized by Banawan and Ulukus, where it was assumed that the messages are encoded and stored separably into the databases. This assumption was also usually taken in other related works in the literature, and this capacity is usually referred to as the MDS-PIR capacity colloquially. In this work, we considered the question if and when this capacity barrier can be broken through joint encoding and storing of the messages. Our main results are two classes…
Data storage systems are more reliable than their individual components. In order to build highly reliable systems out of less reliable parts, systems introduce redundancy. In replicated systems, objects are simply copied several times with each copy residing on a different physical device. While such an approach is simple and direct, more elaborate approaches such as erasure coding can achieve equivalent levels of data protection while using less redundancy. This report examines the trade-offs in cost and performance between replicated and erasure encoded storage systems.
In this paper we study the problem of storing reliably an archive of versioned data. Specifically, we focus on systems where the differences (deltas) between subsequent versions rather than the whole objects are stored - a typical model for storing versioned data. For reliability, we propose erasure encoding techniques that exploit the sparsity of information in the deltas while storing them reliably in a distributed back-end storage system, resulting in improved I/O read performance to retrieve the whole versioned archive. Along with the basic techniques, we propose a few optimization heurist…
In cloud computing, storage area networks, remote backup storage, and similar settings, stored data is modified with updates from new versions. Representing information and modifying the representation are both expensive. Therefore it is desirable for the data to not only be compressed but to also be easily modified during updates. A malleable coding scheme considers both compression efficiency and ease of alteration, promoting codeword reuse. We examine the trade-off between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-measured as the length…
In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a failed node can only be reconstructed from the available live nodes belonging to the available blocks. To analyze the resilience of the system against such block failures, this work introduces the framework of Block Failure Resilient (BFR) codes, wherein the data (e.g., a file in DSS) can be decoded by reading out from a same number of codeword symbols (nodes) …
In this work, we consider a novel distributed data storage/caching scenario in a cellular setting where multiple nodes may fail/depart at the same time. In order to maintain the target reliability, we allow cooperative regeneration of lost nodes with the help of base stations allocated in a set of hierarchical layers. Due to this layered structure, a symbol download from each base station has a different cost, while the link capacities connecting the nodes of the cellular system and the base stations are also limited. In this more practical and general scenario, we present the fundamental trad…
The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. On one end of this spectrum of Regenerating Codes are Minimum Storage Regenerating (MSR) codes that can match the minimum storage cost of MDS codes while also significantly reducing repair bandwidth. In this paper, we describe Exact-MSR codes which allow for any failed nodes (whether they are systematic or parity nodes) to be regenerated exactly rather than only functionally or informatio…
This paper aims to go beyond resilience into the study of security and local-repairability for distributed storage systems (DSS). Security and local-repairability are both important as features of an efficient storage system, and this paper aims to understand the trade-offs between resilience, security, and local-repairability in these systems. In particular, this paper first investigates security in the presence of colluding eavesdroppers, where eavesdroppers are assumed to work together in decoding stored information. Second, the paper focuses on coding schemes that enable optimal local repa…
DNA Data storage has recently attracted much attention due to its durable preservation and extremely high information density (bits per gram) properties. In this work, we propose a hybrid coding strategy comprising of generalized constrained codes to tackle homopolymer (run-length) limit and a protograph based low-density parity-check (LDPC) code to correct asymmetric nucleotide level (i.e., A/T/C/G) substitution errors that may occur in the process of DNA sequencing. Two sequencing techniques namely, Nanopore sequencer and Illumina sequencer with their equivalent channel models and capacities…
We consider the problem of designing codes for distributed storage that protect user data against eavesdroppers that can gain access to network links as well as individual nodes. Our goal is to achieve weak security (also known as block security) that requires that the eavesdroppers would not be able to decode individual files or combinations of a small number of files. The standard approach for achieving block security is to use a joint design scheme that consists of (inner) storage code and the (outer) coset code. However, jointly designing the codes requires that the user, who pre-processes…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an erasure code, in fragments spread across nodes, requires less redundancy than simple replication for the same level of reliability. However, since fragments must be periodically replaced as nodes fail, a key question is how to generate encoded fragments in a distributed way while transferring as little data as possible across the network. For an …
This paper introduces a new source coding paradigm called Sequential Massive Random Access (SMRA). In SMRA, a set of correlated sources is encoded once for all and stored on a server, and clients want to successively access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server is only allowed to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of the specific client's request. In this paper, we formally define the SMRA framework and introduce both storage and transmission rates to characterize the perf…
We consider the problem of secure distributed data storage under the paradigm of \emph{weak security}, in which no \emph{meaningful information} is leaked to the eavesdropper. More specifically, the eavesdropper cannot get any information about any individual message file or a small group of files. The key benefit of the weak security paradigm is that it incurs no loss in the storage capacity, which makes it practically appealing. In this paper, we present a coding scheme, using a coset coding based outer code and a Product-Matrix Minimum Bandwidth Regenerating code (proposed by Rashmi et al.)…
We consider the storage-retrieval rate tradeoff in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook generation and the binning technique is proposed. This coding scheme reveals a hidden connection between PIR and the classic multiple description source coding problem. We first show that when the retrieval rate is kept optimal, the proposed non-linear scheme can achieve better performance over any linear scheme. Moreover, a non-trivial storage-ret…
