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Alberto Ravagnani - IEEE Xplore Author Profile

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We investigate the fundamental limits of the recently proposed random access coverage depth problem for DNA data storage. Under this paradigm, it is assumed that the user information consists of $k$ information strands, which are encoded into $n$ strands via some generator matrix $G$. In the sequencing process, the strands are read uniformly at random, since each strand is available in a large num...Show More
This paper studies two crucial problems in the context of coded distributed storage systems directly related to their performance: 1) for a fixed alphabet size, determine the minimum number of servers the system must have for its service rate region to contain a prescribed set of points; 2) for a given number of servers, determine the minimum alphabet size for which the service rate region of the ...Show More
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some weighted-Hamming-metric codes exhibit the unusual property that all errors beyond half the minimum distance can be corrected. Nevertheless, a tight relation between the error-cor...Show More
We consider the problem of deriving upper bounds on the parameters of sum-rank-metric codes, with focus on their dimension and block length. The sum-rank metric is a combination of the Hamming and the rank metric, and most of the available techniques to investigate it seem to be unable to fully capture its hybrid nature. In this paper, we introduce a new approach based on sum-rank-metric graphs, i...Show More
We consider (symmetric, non-degenerate) bilinear spaces over a finite field and investigate the properties of their $\ell $ -complementary subspaces, i.e., the subspaces that intersect their dual in dimension $\ell $ . This concept generalizes that of a totally isotropic subspace and, in the context of coding theory, specializes to the notions of self-orthogonal, self-dual and linear-complementa...Show More
Distributed storage systems often use locally recoverable codes for easy repair of node failure and batch codes for load balancing. In this survey, we give an expository overview of the service aspects of these two families of codes. Moreover, we revisit different connections between the service rate problem and other relevant concepts in information and coding theory, using tools from finite and ...Show More
We investigate adversarial network coding and decoding focusing on the multishot regime. Errors can occur on a proper subset of the network edges and are modeled via an adversarial channel. The paper contains both bounds and capacity-achieving schemes for the Diamond Network and the Mirrored Diamond Network. We also initiate the study of the generalizations of these networks.Show More
We consider the problem of determining the one-shot, zero-error capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on a mixed-integer program, which computes the size of the largest unambiguous codebook for a given alphabet size. As an application of our approach, we recover, extend and refine various results that were previously obtai...Show More
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical weight distribution. In this context, we establish a duality theorem analogous to (but very different from) a MacWilliams identity. As an application of our results...Show More
We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal framework and a series of techniques to obtain upper and lower bounds on the network’s (1-shot) capacity, improving on the best currently known results. In partic...Show More
We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of such systems within the classical coding theory. We show how we can use the structural properties of the generator matrix defining the scheme to obtain a bounding polytope for the set of data access rates the system can sup...Show More
We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. These lead to two new fundamental parameters of binary error-correcting codes, both of which measure the probability that the maximum likelihood decoder fails. We then derive various bounds for the cardinality...Show More
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection metric. In sharp contrast with the behavior of linear block codes, we show that the typical non-linear code in the Hamming metric of cardinality $q^{n-d+1}$ is far fr...Show More
This paper investigates the theory of sum-rank-metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory of sum-rank-metric codes is also explored, showing that MSRD codes (the sum-rank analogue of MDS codes) dualize to MSRD codes only if all matrix blocks have th...Show More
A combinatorial framework for adversarial network coding is presented. Channels are described by specifying the possible actions that one or more (possibly coordinated) adversaries may take. Upper bounds on three notions of capacity—the one-shot capacity, the zero-error capacity, and the compound zero-error capacity—are obtained for point-to-point channels, and generalized to corresponding capacit...Show More
We propose an algebraic framework for end-to-end physical-layer network coding based on submodules transmission. Our approach is motivated by nested-lattice-based network coding schemes, that naturally induce end-to-end channels where the ambient space has the structure of a module over a principal ideal ring. The setup is compatible with previously proposed approaches for finite chain rings, and ...Show More
Optimal rank-metric codes in Ferrers diagrams are considered. Such codes consist of matrices having zeros at certain fixed positions and can be used to construct good codes in the projective space. First, we consider rank-metric anticodes and prove a code-anticode bound for Ferrers diagram rank-metric codes. The size of optimal linear anticodes is given. Four techniques and constructions of Ferrer...Show More