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The reliability function of memoryless channels with noiseless feedback and variable-length coding has been found to be a linear function of the average rate in the classic work of Burnashev. In this work we consider unifilar channels with noiseless feedback and study specific transmission schemes, the performance of which provides lower bounds for the channel reliability function. In unifilar channels...
Let 1 ≤ s < t, N ≥ 2 be fixed integers and a complex electronic circuit of size t is said to be an s-active, s ≪ t, and can work as a system block if not more than s elements of the circuit are defective. Otherwise, the circuit is said to be an s-defective and should be replaced by a similar s-active circuit. Suppose that there exists a possibility to run N non-adaptive group tests to check the...
Distributed storage systems are known to be susceptible to long tails in response time. It has been shown that in modern online applications such as Bing, Facebook, and Amazon, the long tail of latency is of particular concern, with 99.9th percentile response times being orders of magnitude worse than the mean. As erasure codes emerge as a popular technique in distributed storage to achieve high data...
Boolean network tomography is a powerful tool to infer the state (working/failed) of individual nodes from path-level measurements obtained by egde-nodes. We consider the problem of optimizing the capability of identifying network failures through the design of monitoring schemes. Finding an optimal solution is NP-hard and a large body of work has been devoted to heuristic approaches providing lower...
A procedure to obtain index codes for a given index coding problem by using l-th Near Maximum Distance Separable Codes (NMDS) codes is presented. The advantage of using l-th NMDS codes is the reduction in field size required. A trade off between field size and length of index codes is observed. Using appropriate l-th NMDS codes binary index codes for the index coding problem can be constructed. The...
We derive upper and lower bounds on the secure capacity-memory tradeoff of the K-user (K > 2) wiretap erasure broadcast channel where Kw receivers are weak and have cache memories of equal size, and Ks receivers are strong and have no cache. The bounds coincide for small and large cache memories. The lower bound also exhibits that cache memories provide larger gains under a secrecy constraint than...
This paper considers a K-user Gaussian broadcast channel (BC) where receivers are equipped with cache memories. Lower and upper bounds are established on the capacity-memory tradeoff, i.e., the largest rate achievable for given cache-memories. The lower bound is based on a joint cache-channel coding scheme which generalizes the recently proposed piggyback coding to Gaussian BCs with unequal cache...
A multilevel S-threshold function characterizes a partition of a discrete point set (the domain of the function)into nonempty subsets. Each subset is labeled by one element (level) of the image set. We propose an encoding that converts a multilevel S-threshold function into a tuple of positive integers. The components of this code are generalisation of well known Chow and Nomura parameters. We derive...
We provide a novel upper bound on the rate-distortion function with multiple decoders with side information, which takes the form of a linear program. This complements a recently-obtained lower bound that also takes the form of a linear program. We show that the upper bound is optimal in several instances of the problem1.
The Gaussian parallel relay network, in which two parallel relays assist a source to convey information to a destination, was introduced by Schein and Gallager. An upper bound on the capacity can be obtained by considering broadcast cut between the source and relays and multiple access cut between relays and the destination. Niesen and Diggavi derived an upper bound for Gaussian parallel N-relay network...
This paper studies the one-sided secrecy of a full-duplex two-way wiretap channel. It is motivated by a practical communication scenario, where two legitimate users communicate with each other in the presence of an external eavesdropper and only one of the users wishes to keep its message confidential from the external eavesdropper for the sake of privacy. As a general result, we establish an achievable...
The antidictionary is the set of all minimal forbidden words (MFWs) which never appear in a given input word, and it is useful for data compression, sequence comparison, and so on. In the one-dimensional case, the antidictionaries of periodic sequences are well studied; indeed, a tight upper bound on the length of an MFW and an antidictionary automaton from the antidictionary which can accept any...
In this work, we consider a variant of the set reconciliation problem where the estimate for the size of the symmetric difference may be inaccurate. Given this setup, we propose a new method to reconciling sets of data and we then compare our method to the Invertible Bloom Filter approach proposed by Eppstein et al. [2].
This paper investigates resource allocation algorithms that use limited communication - where the supplier of a resource broadcasts a coordinating signal using one bit of information to users per iteration. Rather than relay anticipated consumption to the supplier, the users locally compute their allocation, while the supplier measures the total resource consumption. Since the users do not compare...
On the one hand, Constraint Satisfaction Problems (CSP) are a declarative and expressive approach for modeling problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances up to millions of variables and clauses. In this article, we present an approach for taking advantage of both CSP modeling and SAT solving. Our technique consists in expressively...
On the one hand, Constraint Satisfaction Problems (CSP) are a declarative and expressive approach for modeling problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances up to millions of variables and clauses. In this article, we present an approach for taking advantage of both CSP modeling and SAT solving. Our technique consists in expressively...
The problems of subspace coding of large cardinality are considered. The main most interesting results which were published to this time are presented. A few directions of the development of this scientific area are mentioned. One of the direction was stated by Koetter, Kschischang and Silva and simultaneously was continued by Gabidulin and Bossert. It is based on so called lifting constructions of...
Discovering useful patterns plays an essential role in data management and data mining. Frequent itemset mining in uncertain transaction databases semantically and computationally differs from traditional techniques applied on (standard) precise transaction databases. Uncertain transaction databases consist of sets of existentially uncertain items. The uncertainty of items in transactions makes traditional...
The Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP) is a generalization of the well known Resource-Constrained Project Scheduling Problem (RCPSP). The most common exact approaches for solving this problem are based on branch-and-bound algorithms, mixed integer linear programming and Boolean satisfiability (SAT). In this paper, we present a new exact approach for solving this problem,...
In this paper, we propose a hybrid symbol mapping scheme, which can be extended to any coded modulation systems with non-binary LDPC coding and high-order modulation. For a given configuration of GF(2p) LDPC code and 2q-QAM signaling, we introduce a bit interleaving pattern for a short block across several coded or modulated symbols, where the interleaved bit indices are allocated according to the...
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