arXiv subjects

Emina Soljanin

Publications and source records attributed to Emina Soljanin.

At least 19 recordsLinked to original sources

arXiv2026

One-at-a-Time Quantum Guessing: Multipartite Entanglement Beyond MoE Games

Multipartite entanglement remains a challenging and not fully understood aspect of quantum information. Monogamy-of-Entanglement (MoE) games have been highly effective for studying limitations on the usefulness of entanglement imposed by monogamy constraints. To better reveal the extent to which multipartite entanglement can be useful, we introduce a class of quantum guessing games, termed One-at-a-Time Guessing (OTG) games. In these games, quantum players individually guess the outcomes of random measurements performed by a referee on a pre-shared entangled state. Unlike MoE games, OTG games select players individually at random according to a specified probability distribution, thereby probing each player's correlation with the referee. We show that, despite monogamy constraints, players sharing certain entangled states can moderately outperform those relying only on classical uncertainty. This advantage arises even in simple OTG games involving only Pauli measurements on qubits, where optimal entanglement increases the winning probability by at least 4%. This contrasts with MoE games, where shared entanglement has been shown in several settings to provide only limited (if any) advantage over classical strategies. We further establish a majorization property: the value of an OTG game respects the majorization ordering of the player-selection probability distribution. We also analyze in detail a two-player OTG game in which the referee measures one of the three Pauli observables on a qubit, and show that it is optimally played using a specific parameterized family of three-qubit $W$-like states. These results suggest that OTG games provide a useful framework for investigating the usefulness of multipartite entanglement in multiparty quantum correlations.

quant-ph↗

arXiv2026

The Oval Strikes Back

We investigate the applications of ovals in projective planes to distributed storage, with a focus on the Service Rate Region problem. Leveraging the incidence relations between lines and ovals, we describe a class of non-systematic MDS matrices with a large number of small and disjoint recovery sets. For certain parameter choices, the service-rate region of these matrices contains the region of a systematic generator matrix for the same code, yielding better service performance. We further apply our construction to analyze the PIR properties of the considered MDS matrices and present a one-step majority-logic decoding algorithm with strong error-correcting capability. These results highlight how ovals, a classical object in finite geometry, re-emerge as a useful tool in modern coding theory.

cs.IT↗

arXiv2026

Majority-Logic Decoding of Binary Locally Recoverable Codes: A Probabilistic Analysis

Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and constructions-have been extensively studied, the performance of LRCs under random erasures and errors has remained largely unexplored. In this work, we study the error- and erasure-correction performance of binary linear LRCs under majority-logic decoding (MLD). Focusing on LRCs with fixed locality and varying availability, we derive explicit upper bounds on the probability of decoding failure over the memoryless Binary Erasure Channel (BEC) and Binary Symmetric Channel (BSC). Our analysis characterizes the behavior of the bit-error rate (BER) and block-error rate (BLER) as functions of the locality and availability parameters. We show that, under mild growth conditions on the availability, the block decoding failure probability vanishes asymptotically, and that majority-logic decoding can successfully correct virtually all of error and erasure patterns of weight linear in the blocklength. The results reveal a substantial gap between worst-case guarantees and typical performance under stochastic channel models.

cs.IT↗

arXiv2025

Universal Maximum Likelihood (List) Decoding via Fast Vector-Matrix Multiplication

Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires $q^{k} n$ operations for an $[n,k]_q$ code. This paper introduces a simple, code-agnostic framework that reduces the worst-case complexity by a factor of $n$, down to $q^{k}$ operations, a highly desirable reduction in practice. The result holds for both linear and nonlinear block codes over general memoryless channels and under both hard-decision and soft-decision decoding. It naturally extends to intersymbol-interference (ISI) channels and ML list decoding with only a negligible increase in complexity. Our core insight is that, upon receipt of each sequence at the receiver, the conditional probability of that sequence for each codeword in the codebook (i.e., the \emph{likelihood}) can be expressed as the inner product of two carefully constructed vectors -- the first depending on the received sequence, and the second on that codeword itself. As a result, evaluating the likelihoods for all codewords in the codebook reduces to a single vector-matrix multiplication, and ML decoding (MLD) becomes the simple task of picking the maximum entry in the resulting vector. The only non-trivial cost lies in the vector-matrix product. However, our matrix construction allows the use of the Mailman algorithm to reduce this cost. This time reduction is achieved at the cost of high space complexity, requiring $\mathcal{O}(q^{k+1} n)$ space to store the pre-computed codebook matrix.

cs.IT↗

arXiv2025

Optimum 1-Step Majority-Logic Decoding of Binary Reed-Muller Codes

The classical majority-logic decoder proposed by Reed for Reed-Muller codes RM(r, m) of order r and length 2^m, unfolds in r+1 sequential steps, decoding message symbols from highest to lowest degree. Several follow-up decoding algorithms reduced the number of steps, but for a limited set of parameters, or at the expense of reduced performance, or relying on the existence of some combinatorial structures. We show that any one-step majority-logic decoder-that is, a decoder performing all majority votes in one step simultaneously without sequential processing-can correct at most d_min/4 errors for all values of r and m, where d_min denotes the code's minimum distance. We then introduce a new hard-decision decoder that completes the decoding in a single step and attains this error-correction limit. It applies to all r and m, and can be viewed as a parallel realization of Reed's original algorithm, decoding all message symbols simultaneously. Remarkably, we also prove that the decoder is optimum in the erasure setting: it recovers the message from any erasure pattern of up to d_min-1 symbols-the theoretical limit. To our knowledge, this is the first 1-step decoder for RM codes that achieves both optimal erasure correction and the maximum one-step error correction capability.

cs.IT↗

arXiv2025

Maximal Achievable Service Rates of Codes and Connections to Combinatorial Designs

We investigate the service-rate region (SRR) of distributed storage systems that employ linear codes. We focus on systems where each server stores one code symbol, and a user recovers a data symbol by accessing any of its recovery groups, subject to per-server capacity limits. The SRR--the convex polytope of simultaneously achievable request rates--captures system throughput and scalability. We first derive upper and lower bounds on the maximum request rate of each data object. These bounds hold for all linear codes and depend only on the number of parity checks orthogonal to a particular set of codeword coordinates associated with that object, i.e., the equations used in majority-logic decoding, and on code parameters. We then check the bound saturation for 1) all non-systematic codes whose SRRs are already known and 2) systematic codes. For the former, we prove the bounds are tight. For systematic codes, we show that the upper bound is achieved whenever the supports of minimum-weight dual codewords form a 2-design. As an application, we determine the exact per-object demand limits for binary Hamming codes. Our framework provides a new lens to address the SRR problem through combinatorial design theory.

cs.IT↗

arXiv2025

On Optimal Batch Size in Coded Computing

We consider computing systems that partition jobs into tasks, add redundancy through coding, and assign the encoded tasks to different computing nodes for parallel execution. The expected execution time depends on the level of redundancy. The computing nodes execute large jobs in batches of tasks. We show that the expected execution time depends on the batch size as well. The optimal batch size that minimizes the execution time depends on the level of redundancy under a fixed number of parallel servers and other system parameters. Furthermore, we show how to (jointly) optimize the redundancy level and batch size to reduce the expected job completion time for two service-time distributions. The simulation presented helps us appreciate the claims.

cs.IT↗

arXiv2025

Service Rate Regions of MDS Codes & Fractional Matchings in Quasi-uniform Hypergraphs

The service rate region (SRR) has emerged as a critical performance metric for distributed systems that store data redundantly. It measures the system's ability to serve multiple users concurrently. Mathematically, the SRR is a polytope in R^k where each dimension corresponds to the service request rate of one of the k data objects. This paper focuses on systems employing a class of Maximum Distance Separable (MDS) codes. For each code in the class, we characterize the k axes intercept points of its SRR, and the smallest standard simplex that includes the SRR. We use these results to show that the SRR grows with the increasing number of systematic columns in the generator matrices. We establish a graph-theoretic framework associating this SRR problem with fractional matchings in quasi-uniform hypergraphs. Identifying the SRR polytope is equivalent to determining a particular image of the fractional-matching polytope. We introduce a notion of Greedy Matching and show that it is sufficient to focus on these matchings to characterize the SRR rather than the entire matching polytope. With these tools, we determine the SRR of a large subset of the considered class of codes. Our results generalize previous characterizations of systematic and non-systematic MDS-coded systems, offering a unified framework for analyzing service rate regions of codes.

cs.IT↗

arXiv2025

On the Redundancy of Function-Correcting Codes over Finite Fields

Function-correcting codes (FCCs) protect specific function evaluations of a message against errors. This condition imposes a less stringent distance requirement than classical error-correcting codes (ECCs), allowing for reduced redundancy. FCCs were introduced by Lenz et al. (2021), who also established a lower bound on the optimal redundancy for FCCs over the binary field. Here, we derive an upper bound within a logarithmic factor of this lower bound. We show that the same lower bound holds for any finite field. Moreover, we show that this bound is tight for sufficiently large fields by demonstrating that it also serves as an upper bound. Furthermore, we construct an encoding scheme that achieves this optimal redundancy. Finally, motivated by these two extreme regimes, we conjecture that our bound serves as a valid upper bound across all finite fields.

cs.IT↗

arXiv2025

Uncertain Location Transmitter and UAV-Aided Warden Based LEO Satellite Covert Communication Systems

We propose a novel covert communication system in which a ground user, Alice, transmits unauthorized message fragments to Bob, a low-Earth orbit satellite (LEO), and an unmanned aerial vehicle (UAV) warden (Willie) attempts to detect these transmissions. The key contribution is modeling a scenario where Alice and Willie are unaware of each other's exact locations and move randomly within a specific area. Alice utilizes environmental obstructions to avoid detection and only transmits when the satellite is directly overhead. LEO satellite technology allows users to avoid transmitting messages near a base station. We introduce two key performance metrics: catch probability (Willie detects and locates Alice during a message chunk transmission) and overall catch probability over multiple message chunks. We analyze how two parameters impact these metrics: 1) the size of the detection window and 2) the number of message chunks. The paper proposes two algorithms to optimize these parameters. The simulation results show that the algorithms effectively reduce the detection risks. This work advances the understanding of covert communication under mobility and uncertainty in satellite-aided systems.

cs.CR↗

arXiv2025

Winning Rates of $(n,k)$ Quantum Coset Monogamy Games

We formulate the $(n,k)$ Coset Monogamy Game, in which two players must extract complementary information of unequal size ($k$ bits vs. $n-k$ bits) from a random coset state without communicating. The complementary information takes the form of random Pauli-X and Pauli-Z errors on subspace states. Our game generalizes those considered in previous works that deal with the case of equal information size $(k=n/2)$. We prove a convex upper bound of the information-theoretic winning rate of the $(n,k)$ Coset Monogamy Game in terms of the subspace rate $R=\frac{k}{n}\in [0,1]$. This bound improves upon previous results for the case of $R=1/2$. We also prove the achievability of an optimal winning probability upper bound for the class of unentangled strategies of the $(n,k)$ Coset Monogamy Game.

quant-ph↗

arXiv2025

On the Service Rate Region of Reed-Muller Codes

We study the Service Rate Region of Reed-Muller codes in the context of distributed storage systems. The service rate region is a convex polytope comprising all achievable data access request rates under a given coding scheme. It represents a critical metric for evaluating system efficiency and scalability. Using the geometric properties of Reed-Muller codes, we characterize recovery sets for data objects, including their existence, uniqueness, and enumeration. This analysis reveals a connection between recovery sets and minimum-weight codewords in the dual Reed-Muller code, providing a framework for identifying those recovery sets. Leveraging these results, we derive explicit and tight bounds on the maximal achievable demand for individual data objects, thereby defining the maximal simplex within the service rate region and the smallest simplex containing it. These two provide a tight approximation of the service rate region of Reed-Muller codes.

cs.IT↗

arXiv2024

Redundancy Management for Fast Service (Rates) in Edge Computing Systems

Edge computing operates between the cloud and end users and strives to provide low-latency computing services for simultaneous users. Redundant use of multiple edge nodes can reduce latency, as edge systems often operate in uncertain environments. However, since edge systems have limited computing and storage resources, directing more resources to some computing jobs will either block the execution of others or pass their execution to the cloud, thus increasing latency. This paper uses the average system computing time and blocking probability to evaluate edge system performance and analyzes the optimal resource allocation accordingly. We also propose blocking probability and average system time optimization algorithms. Simulation results show that both algorithms significantly outperform the benchmark for different service time distributions and show how the optimal replication factor changes with varying parameters of the system.

cs.DC↗

arXiv2024

Optimal Strategies for Winning Certain Coset-Guessing Quantum Games

In a recently introduced coset guessing game, Alice plays against Bob and Charlie, aiming to meet a joint winning condition. Bob and Charlie can only communicate before the game starts to devise a joint strategy. The game we consider begins with Alice preparing a 2m-qubit quantum state based on a random selection of three parameters. She sends the first m qubits to Bob and the rest to Charlie and then reveals to them her choice for one of the parameters. Bob is supposed to guess one of the hidden parameters, Charlie the other, and they win if both guesses are correct. From previous work, we know that the probability of Bob's and Charlie's guesses being simultaneously correct goes to zero exponentially as m increases. We derive a tight upper bound on this probability and show how Bob and Charlie can achieve it. While developing the optimal strategy, we devised an encoding circuit using only CNOT and Hadamard gates, which could be relevant for building efficient CSS-coded systems. We found that the role of quantum information that Alice communicates to Bob and Charlie is to make their responses correlated rather than improve their individual (marginal) correct guessing rates.

quant-ph↗

arXiv2024

The Service Rate Region Polytope

We investigate the properties of a family of polytopes that naturally arise in connection with a problem in distributed data storage, namely service rate region polytopes. The service rate region of a distributed coded system describes the data access requests that the underlying system can support. In this paper, we study the polytope structure of the service rate region with the primary goal of describing its geometric shape and properties. We achieve so by introducing various structural parameters of the service rate region and establishing upper and lower bounds for them. The techniques we apply in this paper range from coding theory to optimization. One of our main results shows that every rational point of the service rate region has a so-called rational allocation, answering an open question in the research area.

math.OC↗

arXiv2024

On the Parameters of Codes for Data Access

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 system contains a prescribed set of points. The paper establishes rigorous upper and lower bounds, as well as code constructions based on techniques from coding theory, optimization, and projective geometry.

cs.IT↗

arXiv2023

Controlling Data Access Load in Distributed Systems

Distributed systems store data objects redundantly to balance the data access load over multiple nodes. Load balancing performance depends mainly on 1) the level of storage redundancy and 2) the assignment of data objects to storage nodes. We analyze the performance implications of these design choices by considering four practical storage schemes that we refer to as clustering, cyclic, block and random design. We formulate the problem of load balancing as maintaining the load on any node below a given threshold. Regarding the level of redundancy, we find that the desired load balance can be achieved in a system of $n$ nodes only if the replication factor $d = Ω(\log(n)^{1/3})$, which is a necessary condition for any storage design. For clustering and cyclic designs, $d = Ω(\log(n))$ is necessary and sufficient. For block and random designs, $d = Ω(\log(n))$ is sufficient but unnecessary. Whether $d = Ω(\log(n)^{1/3})$ is sufficient remains open. The assignment of objects to nodes essentially determines which objects share the access capacity on each node. We refer to the number of nodes jointly shared by a set of objects as the \emph{overlap} between those objects. We find that many consistently slight overlaps between the objects (block, random) are better than few but occasionally significant overlaps (clustering, cyclic). However, when the demand is ''skewed beyond a level'' the impact of overlaps becomes the opposite. We derive our results by connecting the load-balancing problem to mathematical constructs that have been used to study other problems. For a class of storage designs containing the clustering and cyclic design, we express load balance in terms of the maximum of moving sums of i.i.d. random variables, which is known as the scan statistic. For random design, we express load balance by using the occupancy metric for random allocation with complexes.

cs.DC↗

arXiv2023

Theory vs. Practice in Modeling Edge Storage Systems

Edge systems promise to bring data and computing closer to the users of time-critical applications. Specifically, edge storage systems are emerging as a new system paradigm, where users can retrieve data from small-scale servers inter-operating at the network's edge. The analysis, design, and optimization of such systems require a tractable model that will reflect their costs and bottlenecks. Alas, most existing mathematical models for edge systems focus on stateless tasks, network performance, or isolated nodes and are inapplicable for evaluating edge-based storage performance. We analyze the capacity-region model - the most promising model proposed so far for edge storage systems. The model addresses the system's ability to serve a set of user demands. Our analysis reveals five inherent gaps between this model and reality, demonstrating the significant remaining challenges in modeling storage service at the edge.

cs.DC↗