Vitaly Skachek

Vitaly Skachek
University of Tartu · Institute of Computer Science

About

90
Publications
6,461
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848
Citations

Publications

Publications (90)
Article
Full-text available
Assume a distributed system with two users, each user possesses a collection of binary strings. We introduce a new problem termed function computation on the reconciled data, which generalizes a set reconciliation problem in the literature. It is shown that any deterministic protocol that computes a sum and a product of reconciled sets of nonnegati...
Article
Full-text available
Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $l$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping sets of size up to $\ell$. In this work, a notion of coverable stopping sets is defined. In order to achieve maxi...
Preprint
Full-text available
We propose a new model of asynchronous batch codes that allow for parallel recovery of information symbols from a coded database in an asynchronous manner, i.e. when queries arrive at random times and they take varying time to process. We show that the graph-based batch codes studied by Rawat et al. are asynchronous. Further, we demonstrate that hy...
Preprint
Full-text available
Invertible Bloom Filter (IBF) is a data structure, which employs a small set of hash functions. An IBF allows for an efficient insertion and, with high probability, for an efficient extraction of the data. However, the success probability of the extraction depends on the storage overhead of an IBF and the amount of the data stored. In an applicatio...
Article
We propose a new model of asynchronous batch codes that allow for parallel recovery of information symbols from a coded database in an asynchronous manner, i.e. when requests arrive at random times and they take varying time to process. We show that the graph-based batch codes studied by Rawat et al. are asynchronous. Further, we demonstrate that h...
Preprint
Full-text available
The binary $k$-dimensional simplex code is known to be a $2^{k-1}$-batch code and is conjectured to be a $2^{k-1}$-functional batch code. Here, we offer a simple, constructive proof of a result that is "in between" these two properties. Our approach is to relate these properties to certain (old and new) additive problems in finite abelian groups. W...
Preprint
The goal of the paper is to study specific properties of nonbinary low-density parity-check (NB LDPC) codes when used in coded modulation systems. The paper is focused on the practically important NB LDPC codes over extensions of the Galois field GF$(2^m)$ with $m \le 6$ used with QAM signaling. Performance of NB QC LDPC coded transmission strongly...
Preprint
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code Tanner graph. Tightened random coding bounds based on the average...
Book
Full-text available
In 1989 we organized the first Benelux‐Japan workshop on Information and Communication theory in Eindhoven, the Netherlands. This year, 2019 we celebrate 30 years of our friendship between Asian and European scientists at the AEW11 in Rotterdam, the Netherlands. Many of the 1989 participants are also present at the 2019 event. This year we have man...
Preprint
Full-text available
This year, 2019 we celebrate 30 years of our friendship between Asian and European scientists at the AEW11 in Rotterdam, the Netherlands. Many of the 1989 participants are also present at the 2019 event. This year we have many participants from different parts of Asia and Europe. It shows the importance of this event. It is a good tradition to pay...
Preprint
Full-text available
We propose a new model of asynchronous batch codes that allow for parallel recovery of information symbols from a coded database in an asynchronous manner, i.e. when different queries take different time to process. Then, we show that the graph-based batch codes studied in Rawat et al., IEEE Trans. on Inform. Theory, Apr. 2016, are asynchronous. Fu...
Chapter
Two related families of codes are studied: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. Bounds on the parameters of the codes, as well a...
Article
Full-text available
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is computed by using a recurrent procedure and compared to the empirically found average spectrum for the same ensem...
Conference Paper
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied...
Conference Paper
Linear batch codes and codes for private information retrieval (PIR) with a query size t and a restricted size r of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of t or r by providing corresponding constructions. By building on the ideas of Cadambe and Mazumdar, a new bound in a recurs...
Article
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML decoding over a BEC and an AWGN channel are studied. Both random and structured LDPC codes are considered. In particular, the BP decoding is applied...
Article
Full-text available
A new method for low-complexity near-maximum-likelihood (ML) decoding of low-density parity-check (LDPC) codes over the additive white Gaussian noise channel is presented. The proposed method termed belief-propagation--list erasure decoding (BP-LED) is based on erasing carefully chosen unreliable bits performed in case of BP decoding failure. A str...
Article
Full-text available
Future networks are expected to depart from traditional routing schemes in order to embrace network coding (NC)-based schemes. These have created a lot of interest both in academia and industry in recent years. Under the NC paradigm, symbols are transported through the network by combining several information streams originating from the same or di...
Article
Linear batch codes and codes for private information retrieval (PIR) with a query size $t$ and a restricted size $r$ of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of $t$ or of $r$ by providing corresponding constructions. By building on the ideas of Cadambe and Mazumdar, a new bound...
Book
This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017. The 24 full papers presented were carefully reviewed and selected for inclusion in this volume. The papers cover relevant research areas in modern coding theory, including co...
Article
In this survey, we discuss two related families of codes: batch codes and codes for private information retrieval (PIR codes). These two families can be viewed as natural generalizations of locally-repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. For the sake of compl...
Conference Paper
Full-text available
The energy efficiency of a system determines its operational sustainability. Energy harvesting (EH) is a crucial technology for a variety of wireless systems that have limited access to a reliable electricity supply. In this paper, the design of a multiple access relay system (MARS) using EH is considered. We assume that the sources and relay have...
Article
Full-text available
In forthcoming years, the Internet of Things (IoT) will connect billions of smart devices generating and uploading a deluge of data to the cloud. If successfully extracted, the knowledge buried in the data can significantly improve the quality of life and foster economic growth. However, a critical bottleneck for realising the efficient IoT is the...
Article
We consider the transmission and storage of data that use coded binary symbols over a channel, where a Pearsondistance-based detector is used for achieving resilience against additive noise, unknown channel gain, and varying offset. We study Minimum Pearson Distance (MPD) detection in conjunction with a set, S, of codewords satisfying a center-of-m...
Conference Paper
The 3GPP machine type communications (MTC) service is expected to contribute a dominant share of the IoT traffic via the upcoming fifth generation (5G) mobile cellular systems. MTC has ambition to connect billions of devices to communicate their data to MTC applications for further processing and data analysis. However, for majority of the applicat...
Conference Paper
A novel method of low-complexity near-maximum-likelihood (ML) decoding of quasi-cyclic (QC) low-density parity-check (LDPC) codes over the binary erasure channel is presented. The idea is similar to wrap-around decoding of tail-biting convolutional codes. ML decoding is applied to a relatively short window which is cyclically shifted along the rece...
Conference Paper
Full-text available
This paper proposes a new technique of spatially-coupled low-density parity-check (SC-LDPC) code-based soft information relaying scheme for a two-way relay system. We introduce an optimized SC-LDPC codes in relay channels. A more precise model is proposed to characterize the soft noise on the soft symbols, using a pre-calculated look-up table at th...
Article
Full-text available
This paper proposes a novel technique of {spatially-coupled low-density parity-check (SC-LDPC) code-based soft forwarding relaying scheme for a two-way relay system. We introduce an array based optimized SC-LDPC codes in relay channels. A more precise model is proposed to characterize the residual noise on the soft symbols, using a pre-calculated l...
Article
Full-text available
We present new upper bounds on the parameters of batch codes with restricted query size. These bounds are an improvement on the Singleton bound. The techniques for derivations of these bounds are based on the ideas in the literature for codes with locality. By employing additional ideas, we obtain further improvement on the bounds obtained for the...
Article
Full-text available
New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths. Second, several probabilistic lower bounds are developed, which improve on the known lower bounds for large minim...
Article
Full-text available
In this work, we formulate and study a data dissemination problem, which can be viewed as a generalization of the index coding problem and of the data exchange problem to networks with an arbitrary topology. We define $r$-solvable networks, in which data dissemination can be achieved in $r > 0$ communications rounds. We show that the optimum number...
Article
The $l$-th stopping redundancy $\rho_l(\mathcal C)$ of the binary $[n, k, d]$ code $\mathcal C$, $1 \le l \le d$, is defined as the minimum number of rows in the parity-check matrix of $\mathcal C$, such that the smallest stopping set is of size at least $l$. The stopping redundancy $\rho(\mathcal C)$ is defined as $\rho_d(\mathcal C)$. In this wor...
Article
Associative memories are widely used devices which can be viewed as universal error-correcting decoders. Employing error-correcting code principles in these devices has allowed to greatly enhance their performance. In this paper we reintroduce a neural-based model using the formalism of linear algebra and extend its functionality, originally limite...
Conference Paper
Assume that two users possess two different subspaces of an ambient linear space. We show that the problem of synchronization of such vector spaces can be easily solved by an efficient algorithm. By building on this observation, we propose an algorithm for synchronization of two collections of binary files of length n each, stored in the cloud in a...
Article
In this article, we study properties and algorithms for constructing sets of 'constant weight' codewords with bipolar symbols, where the sum of the symbols is a constant q, q 6 0. We show various code constructions that extend Knuth's balancing vector scheme, q = 0, to the case where q > 0. We compute the redundancy of the new coding methods. Index...
Article
Full-text available
In an application, where a client wants to obtain many symbols from a large database, it is often desirable to balance the load. Batch codes (introduced by Ishai et al. in STOC 2004) do exactly that: the large database is divided between many servers, so that the client has to only make a small number of queries to every server to obtain sufficient...
Article
The min-rank of a digraph was shown to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this paper, the graphs and digraphs of near-extreme min-ranks are studied. Those graphs and digraphs correspond to the ICSI instances having near-extreme transmis...
Conference Paper
We study the use of sparse structured associative memories as a memory-efficient and computationally-efficient data structure for representing a set of elements when one wishes to perform set-membership queries and some errors (false positives) are tolerable. Associative memories, when viewed as representing a set, enjoy a number of interesting pro...
Conference Paper
We consider the problem of efficient and lossless representation of a multiset of m words drawn with repetition from a set of size 2n. One expects that encoding the (unordered) multiset should lead to significant savings in rate as compared to encoding an (ordered) sequence with the same words, since information about the order of words in the sequ...
Conference Paper
A new family of associative memories based on sparse neural networks has been recently introduced. These memories achieve excellent performance thanks to the use of error-correcting coding principles. In this work, we introduce a new family of codes termed clique codes. These codes are based on the cliques in balanced n-partite graphs describing as...
Conference Paper
Full-text available
We consider rank modulation codes for flash memories that allow for handling arbitrary charge drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed translocation codes account for more general forms of errors that arise in storage systems. Tra...
Article
Full-text available
Security aspects of the index coding with side information (ICSI) problem are investigated. Building on the results of Bar-Yossef (2006), the properties of linear index codes are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is shown t...
Article
Full-text available
The min-rank of a digraph was shown by Bar-Yossef et al. (2006) to represent the length of an optimal scalar linear solution of the corresponding instance of the Index Coding with Side Information (ICSI) problem. In this work, the graphs and digraphs of near-extreme min-ranks are characterized. Those graphs and digraphs correspond to the ICSI insta...
Article
Full-text available
We consider rank modulation codes for flash memories that allow for handling arbitrary charge-drop errors. Unlike classical rank modulation codes used for correcting errors that manifest themselves as swaps of two adjacently ranked elements, the proposed \emph{translocation rank codes} account for more general forms of errors that arise in storage...
Conference Paper
Full-text available
Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (2006), the properties of linear index codes are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized to block security. It is...
Article
Full-text available
We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a significantly large number of different basis vectors transmitted through the network and when the min-cut of t...
Article
Full-text available
A linear-programming decoder for nonbinary expander codes is presented. It is shown that the proposed decoder has the nearest-neighbor certificate properties. It is also shown that this decoder corrects any pattern of errors of a relative weight up to approximately 1/4δ<sub>A</sub>δ<sub>B</sub> (where δ<sub>A</sub> and δ<sub>B</sub> are the relativ...
Article
Full-text available
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied. Error-correcting methods for such a scheme, and their parameters, are investigated. In particular, the following q...
Article
Full-text available
The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of the code. It is shown that most codes do not have a finite pseudocodeword redundancy. Also, upper b...
Article
Full-text available
A problem of index coding with side information was first considered by Y. Birk and T. Kol (IEEE INFOCOM, 1998). In the present work, a generalization of index coding scheme, where transmitted symbols are subject to errors, is studied. Error-correcting methods for such a scheme, and their parameters, are investigated. In particular, the following q...
Article
Full-text available
Security aspects of the Index Coding with Side Information (ICSI) problem are investigated. Building on the results of Bar-Yossef et al. (2006), the properties of linear coding schemes for the ICSI problem are further explored. The notion of weak security, considered by Bhattad and Narayanan (2005) in the context of network coding, is generalized t...
Conference Paper
Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when viewed as points in the multidimensional Euclidean space, lie inside a fundamental cone. This fundamental con...
Article
Full-text available
Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when viewed as points in the multidimensional Euclidean space, lie inside a fundamental cone. This fundamental con...
Conference Paper
Full-text available
We define the AWGNC, BSC, and max-fractional pseudocodeword redundancy p(C) of a code C as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of C. We show that most codes do not have a finite p(C). We also provide bounds on the pseudocodeword redundancy for...
Article
Full-text available
The AWGNC, BSC, and max-fractional pseudocodeword redundancy of a code is defined as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the minimum Hamming distance of the code. This paper provides new results on the AWGNC, BSC, and max-fractional pseudocodeword redundancies of codes. T...
Conference Paper
A linear-programming (LP) decoder for nonbinary expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a relative weight up to approximately 1/4delta<sub>A</sub>delta<sub>B</sub> (where delta<sub>A</sub> and delta<sub>...
Article
Full-text available
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a Singleton bound. We also present some families of codes meeting these new bounds.
Conference Paper
Full-text available
We present lower bounds on the minimum pseudocodeword effective Euclidean distance (or minimum ldquopseudodistancerdquo) for coded modulation systems using linear codes with q-ary phase-shift keying (PSK) modulation over the additive white Gaussian noise (AWGN) channel. These bounds apply to both binary and nonbinary coded modulation systems which...
Article
Full-text available
A probabilistic algorithm is presented for finding a basis of the root space of a linearized polynomial $$L(x) = \sum_{i=0}^t L_i x^{q^i}
Article
Full-text available
A modification of Koetter-Kschischang codes for random networks is presented (these codes were also studied by Wang et al. in the context of authentication problems). The new codes have higher information rate, while maintaining the same error-correcting capabilities. An efficient error-correcting algorithm is proposed for these codes. Comment: Sub...
Article
Full-text available
A framework for linear-programming (LP) decoding of nonbinary linear codes over rings is developed. This framework facilitates linear-programming based reception for coded modulation systems which use direct modulation mapping of coded symbols. It is proved that the resulting LP decoder has the 'maximum-likelihood certificate' property. It is also...
Article
Full-text available
In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many classes of codes these polytopes yield a complexity advantage for decoding. These representations lead to polynom...
Conference Paper
Full-text available
Several expander code constructions and their parameters are surveyed. New generalized expander codes are introduced and their properties are compared with the properties of the existing constructions. Finally, some possible directions to extend the current research on expander codes are discussed.
Article
Full-text available
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the 'maximum likelihood certifi cate' property, and we show that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph co...
Article
Full-text available
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small decoding error probability. Specifically, it is assumed that there exists a family of codes of length N and ra...
Article
Full-text available
A construction of expander codes is presented with the following three properties: i) the codes lie close to the Singleton bound, ii) they can be encoded in time complexity that is linear in their code length, and iii) they have a linear-time bounded-distance decoder. By using a version of the decoder that corrects also erasures, the codes can repl...
Conference Paper
Full-text available
A construction of graph codes is presented that approaches the singleton bound as the alphabet size goes to infinity. These codes can be decoded by a combined error-erasure decoder whose time complexity grows linearly with the code length.
Conference Paper
Recently, G. Zemor (see IEEE Trans. Inf. Theory, vol.47, p.835-7, 2001) proposed an improvement on the Sipser-Spielman analysis of expander codes (Sipser, M. and Spielman, D.A., IEEE Trans. Inf. Theory, vol.42 , p.1710-22, 1996) and presented a linear-time iterative decoder that can correct a number of errors up to approximately 1/4 the known lower...