arXiv subjects

Derya Malak

Publications and source records attributed to Derya Malak.

At least 19 recordsLinked to original sources

arXiv2026

Multi-User Non-Linearly Separable Distributed Computing

This paper considers an $N$-server distributed computing setting with $K$ users requesting functions that are arbitrary multivariable polynomial evaluations of $L$ real (potentially non-linear) basis subfunctions, where each function output is raised to a bounded power. Our aim is to seek efficient task allocation and data communication techniques that reduce computation and communication costs. To this end, we take a tensor-theoretic approach, in which we represent the requested non-linearly decomposable functions using a properly designed tensor $\bar{\mathcal{F}}$, whose sparse decomposition into a tensor $\bar{\mathcal{E}}$ and a matrix $\mathbf{D}$ directly defines the task assignment, connectivity, and communication patterns. We design a lossless achievable scheme that integrates fixed-support SVD-based tensor factorization with multi-dimensional tiling of $\bar{\mathcal{E}}$ and $\mathbf{D}$, followed by a bipartite graph matching-based recursive assignment of tiles. This step transforms an overlapping decomposition into a disjoint one and reduces the resulting sum rank of the tiles, thereby decreasing the number of required servers. Under mild dimensionality conditions, we derive an explicit zero-error characterization of the achievable system rate $K/N$. Numerical simulations demonstrate the computational and communication savings over existing state-of-the-art matrix factorization approaches across a wide range of system parameters.

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arXiv2026

Fundamental Limits of Multi-User Distributed Computing of Linearly Separable Functions

This work establishes the fundamental limits of the classical problem of multi-user distributed computing of linearly separable functions. In particular, we consider a distributed computing setting involving $L$ users, each requesting a linearly separable function over $K$ basis subfunctions from a master node, who is assisted by $N$ distributed servers. At the core of this problem lies a fundamental tradeoff between communication and computation: each server can compute up to $M$ subfunctions, and each server can communicate linear combinations of their locally computed subfunctions outputs to at most $\Delta$ users. The objective is to design a distributed computing scheme that reduces the communication cost (total amount of data from servers to users), and towards this, for any given $K$, $L$, $M$, and $\Delta$, we propose a distributed computing scheme that jointly designs the task assignment and transmissions, and shows that the scheme achieves optimal performance in the real field under various conditions using a novel converse. We also characterize the performance of the scheme in the finite field using another converse based on counting arguments.

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arXiv2026

Learning-Augmented Perfectly Secure Collaborative Matrix Multiplication

This paper presents a perfectly secure matrix multiplication (PSMM) protocol for multiparty computation (MPC) of $\mathrm{A}^{\top}\mathrm{B}$ over finite fields. The proposed scheme guarantees correctness and information-theoretic privacy against threshold-bounded, semi-honest colluding agents, under explicit local storage constraints. Our scheme encodes submatrices as evaluations of sparse masking polynomials and combines coefficient alignment with Beaver-style randomness to ensure perfect secrecy. We demonstrate that any colluding set of parties below the security threshold observes uniformly random shares, and that the recovery threshold is optimal, matching existing information-theoretic limits. Building on this framework, we introduce a learning-augmented extension that integrates tensor-decomposition-based local block multiplication, capturing both classical and learned low-rank methods. We demonstrate that the proposed learning-based PSMM preserves privacy and recovery guarantees for MPC, while providing scalable computational efficiency gains (up to $80\%$) as the matrix dimensions grow.

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arXiv2025

Fundamental Limits of Distributed Computing for Linearly Separable Functions

This work addresses the problem of distributed computation of linearly separable functions, where a master node with access to $K$ datasets, employs $N$ servers to compute $L$ user-requested functions, each defined over the datasets. Servers are instructed to compute subfunctions of the datasets and must communicate computed outputs to the user, who reconstructs the requested outputs. The central challenge is to reduce the per-server computational load and the communication cost from servers to the user, while ensuring recovery for any possible set of $L$ demanded functions. We here establish the fundamental communication-computation tradeoffs for arbitrary $K$ and $L$, through novel task-assignment and communication strategies that, under the linear-encoding and no-subpacketization assumptions, are proven to be either exactly optimal or within a factor of three from the optimum. In contrast to prior approaches that relied on fixed assignments of tasks -- either disjoint or cyclic assignments -- our key innovation is a nullspace-based design that jointly governs task assignment and server transmissions, ensuring exact decodability for all demands, and attaining optimality over all assignment and delivery methods. To prove this optimality, we here uncover a duality between nullspaces and sparse matrix factorizations, enabling us to recast the distributed computing problem as an equivalent factorization task and derive a sharp information-theoretic converse bound. Building on this, we establish an additional converse that, for the first time, links the communication cost to the covering number from the theory of general covering designs.

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arXiv2025

Distributed Compression for Computation and Bounds on the Optimal Rate

We address the problem of distributed computation of arbitrary functions of two correlated sources $X_1$ and $X_2$, residing in two distributed source nodes, respectively. We exploit the structure of a computation task by coding source characteristic graphs (and multiple instances using the $n$-fold OR product of this graph with itself). For regular graphs and general graphs, we establish bounds on the optimal rate -- characterized by the chromatic entropy for the $n$-fold graph products -- that allows a receiver for asymptotically lossless computation of arbitrary functions over finite fields. For the special class of cycle graphs (i.e., $2$-regular graphs), we establish an exact characterization of chromatic numbers and derive bounds on the required rates. Next, focusing on the more general class of $d$-regular graphs, we establish connections between $d$-regular graphs and expansion rates for $n$-fold graph powers using graph spectra. Finally, for general graphs, we leverage the Gershgorin Circle Theorem (GCT) to provide a characterization of the spectra, which allows us to build new bounds on the optimal rate. Our codes leverage the spectra of the computation and provide a graph expansion-based characterization to efficiently/succinctly capture the computation structure, providing new insights into the problem of distributed computation of arbitrary functions.

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arXiv2025

Non-Linear Function Computation Broadcast

This work addresses the $K$-user computation broadcast problem consisting of a master node, that holds all datasets and users for a general class of function demands, including linear and non-linear functions, over finite fields. The master node sends a broadcast message to enable each of $K$ distributed users to compute its demanded function in an asymptotically lossless manner with user's side information. We derive bounds on the optimal $K$-user computation broadcast rate that allows the users to compute their demanded functions by capturing the structures of the computations and available side information. Our achievability scheme involves the design of a novel graph-based coding model to build a broadcast message to meet each user's demand, by leveraging the structural dependencies among the datasets, the user demands, and the side information of each user, drawing on K{ö}rner's characteristic graph framework. The converse uses the structures of the demands and the side information available at $K$ users to yield a tight lower bound on the broadcast rate. With the help of examples, we demonstrate our scheme achieves a better communication rate than the existing state of the art.

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arXiv2024

Structured Codes for Distributed Matrix Multiplication

Our work addresses the well-known open problem of distributed computing of bilinear functions of two correlated sources ${\bf A}$ and ${\bf B}$. In a setting with two nodes, with the first node having access to ${\bf A}$ and the second to ${\bf B}$, we establish bounds on the optimal sum rate that allows a receiver to compute an important class of non-linear functions, and in particular bilinear functions, including dot products $\langle {\bf A},{\bf B}\rangle$, and general matrix products ${\bf A}^{\intercal}{\bf B}$ over finite fields. The bounds are tight for large field sizes, for which case we can derive the exact fundamental performance limits for all problem dimensions and a large class of sources. Our achievability scheme involves the design of non-linear transformations of ${\bf A}$ and ${\bf B}$, carefully calibrated to work synergistically with the structured linear encoding scheme by K\"orner and Marton. The subsequent converses derived here, calibrate the Han-Kobayashi approach and the strong converse of Ahlswede-G\'acs-K\"orner to yield relatively tight converses on the sum rate. We exhibit unbounded compression gains over Slepian-Wolf coding, depending on the source correlations. In the end, this work characterizes the fundamental limits of distributed computing for a crucial class of functions, while succinctly capturing the inherent computation structures and source correlations.

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arXiv2024

The Influence of Placement on Transmission in Distributed Computing of Boolean Functions

In this paper, we explore a distributed setting, where a user seeks to compute a linearly-separable Boolean function of degree $M$ from $N$ servers, each with a cache size $M$. Exploiting the fundamental concepts of sensitivity and influences of Boolean functions, we devise a novel approach to capture the interplay between dataset placement across servers and server transmissions and to determine the optimal solution for dataset placement that minimizes the communication cost. In particular, we showcase the achievability of the minimum average joint sensitivity, $\frac{N}{2^{M-1}}$, as a measure for the communication cost.

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arXiv2024

Distributed Structured Matrix Multiplication

We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our approach relies on devising nonlinear mappings of distributed sources, which are then followed by the structured linear encoding scheme, introduced by Körner and Marton. For different computation scenarios, we contrast our findings on the achievable sum rate with the state of the art to demonstrate the possible savings in compression rate. When the sources have special correlation structures, it is possible to achieve unbounded gains, as demonstrated by the analysis and numerical simulations.

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arXiv2024

Multi-Server Multi-Function Distributed Computation

The work here studies the communication cost for a multi-server multi-task distributed computation framework, and does so for a broad class of functions and data statistics. Considering the framework where a user seeks the computation of multiple complex (conceivably non-linear) tasks from a set of distributed servers, we establish communication cost upper bounds for a variety of data statistics, function classes and data placements across the servers. To do so, we proceed to apply, for the first time here, Körner's characteristic graph approach -- which is known to capture the structural properties of data and functions -- to the promising framework of multi-server multi-task distributed computing. Going beyond the general expressions, and in order to offer clearer insight, we also consider the well-known scenario of cyclic dataset placement and linearly separable functions over the binary field, in which case our approach exhibits considerable gains over the state of art. Similar gains are identified for the case of multi-linear functions.

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arXiv2024

The Interplay of Spectral Efficiency, User Density, and Energy in Grant-based Access Protocols

We employ grant-based access with retransmissions for multiple users with small payloads, particularly at low spectral efficiency (SE). The radio resources are allocated via NOMA in the time into $T$ slots and frequency dimensions, with a measure of non-orthogonality $η$. Retransmissions are stored in a receiver buffer with a finite size $C_{\sf buf}$ and combined via HARQ, using Chase Combining (CC) and Incremental Redundancy (IR). We determine the best scaling for the SE (bits/rdof) and for the user density $J/n$, for a given number of users $J$ and a blocklength $n$, versus SNR ($ρ$) per bit, i.e., the ratio $E_b/N_0$, for the sum-rate optimal regime and when the interference is treated as noise (TIN), using a finite blocklength analysis. Contrasting the classical scheme (no retransmissions) with CC-NOMA, CC-OMA, and IR-OMA strategies in TIN and sum-rate optimal cases, the numerical results on the SE demonstrate that CC-NOMA outperforms, almost in all regimes, the other approaches. In the sum-rate optimal regime, the scalings of $J/n$ versus $E_b/N_0$ deteriorate with $T$, yet from the most degraded to the least, the ordering of the schemes is as (i) classical, (ii) CC-OMA, (iii) IR-OMA, and (iv) CC-NOMA, demonstrating the robustness of CC-NOMA. Contrasting TIN models at low $ρ$, the scalings of $J/n$ for CC-based models improve the best, whereas, at high $ρ$, the scaling of CC-NOMA is poor due to higher interference, and CC-OMA becomes prominent due to combining retransmissions and its reduced interference. The scaling results are applicable over a range of $η$, $T$, $C_{\sf buf}$, and $J$, at low received SNR. The proposed analytical framework provides insights into resource allocation in grant-based access and specific 5G use cases for massive URLLC uplink access.

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arXiv2023

Distributed Computing of Functions of Structured Sources with Helper Side Information

In this work, we consider the problem of distributed computing of functions of structured sources, focusing on the classical setting of two correlated sources and one user that seeks the outcome of the function while benefiting from low-rate side information provided by a helper node. Focusing on the case where the sources are jointly distributed according to a very general mixture model, we here provide an achievable coding scheme that manages to substantially reduce the communication cost of distributed computing by exploiting the nature of the joint distribution of the sources, the side information, as well as the symmetry enjoyed by the desired functions. Our scheme -- which can readily apply in a variety of real-life scenarios including learning, combinatorics, and graph neural network applications -- is here shown to provide substantial reductions in the communication costs, while simultaneously providing computational savings by reducing the exponential complexity of joint decoding techniques to a complexity that is merely linear.

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arXiv2023

Weighted Graph Coloring for Quantized Computing

We consider the problem of distributed lossless computation of a function of two sources by one common user. To do so, we first build a bipartite graph, where two disjoint parts denote the individual source outcomes. We then project the bipartite graph onto each source to obtain an edge-weighted characteristic graph (EWCG), where edge weights capture the function's structure, by how much the source outcomes are to be distinguished, generalizing the classical notion of characteristic graphs. Via exploiting the notions of characteristic graphs, the fractional coloring of such graphs, and edge weights, the sources separately build multi-fold graphs that capture vector-valued source sequences, determine vertex colorings for such graphs, encode these colorings, and send them to the user that performs minimum-entropy decoding on its received information to recover the desired function in an asymptotically lossless manner. For the proposed EWCG compression setup, we characterize the fundamental limits of distributed compression, verify the communication complexity through an example, contrast it with traditional coloring schemes, and demonstrate that we can attain compression gains higher than $\% 30$ over traditional coloring.

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arXiv2023

A Distributed Computationally Aware Quantizer Design via Hyper Binning

We design a distributed function-aware quantization scheme for distributed functional compression. We consider $2$ correlated sources $X_1$ and $X_2$ and a destination that seeks an estimate $\hat{f}$ for the outcome of a continuous function $f(X_1,\,X_2)$. We develop a compression scheme called hyper binning in order to quantize $f$ via minimizing the entropy of joint source partitioning. Hyper binning is a natural generalization of Cover's random code construction for the asymptotically optimal Slepian-Wolf encoding scheme that makes use of orthogonal binning. The key idea behind this approach is to use linear discriminant analysis in order to characterize different source feature combinations. This scheme captures the correlation between the sources and the function's structure as a means of dimensionality reduction. We investigate the performance of hyper binning for different source distributions and identify which classes of sources entail more partitioning to achieve better function approximation. Our approach brings an information theory perspective to the traditional vector quantization technique from signal processing.

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arXiv2022

FlEC: Enhancing QUIC with application-tailored reliability mechanisms

Packet losses are common events in today's networks. They usually result in longer delivery times for application data since retransmissions are the de facto technique to recover from such losses. Retransmissions is a good strategy for many applications but it may lead to poor performance with latency-sensitive applications compared to network coding. Although different types of network coding techniques have been proposed to reduce the impact of losses by transmitting redundant information, they are not widely used. Some niche applications include their own variant of Forward Erasure Correction (FEC) techniques, but there is no generic protocol that enables many applications to easily use them. We close this gap by designing, implementing and evaluating a new Flexible Erasure Correction (FlEC) framework inside the newly standardized QUIC protocol. With FlEC, an application can easily select the reliability mechanism that meets its requirements, from pure retransmissions to various forms of FEC. We consider three different use cases: $(i)$ bulk data transfer, $(ii)$ file transfers with restricted buffers and $(iii)$ delay-constrained messages. We demonstrate that modern transport protocols such as QUIC may benefit from application knowledge by leveraging this knowledge in FlEC to provide better loss recovery and stream scheduling. Our evaluation over a wide range of scenarios shows that the FlEC framework outperforms the standard QUIC reliability mechanisms from a latency viewpoint.

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arXiv2022

Fractional Graph Coloring for Functional Compression with Side Information

We describe a rational approach to reduce the computational and communication complexities of lossless point-to-point compression for computation with side information. The traditional method relies on building a characteristic graph with vertices representing the source symbols and with edges that assign a source symbol to a collection of independent sets to be distinguished for the exact recovery of the function. Our approach uses fractional coloring for a b-fold coloring of characteristic graphs to provide a linear programming relaxation to the traditional coloring method and achieves coding at a fine-grained granularity. We derive the fundamental lower bound for compression, given by the fractional characteristic graph entropy, through generalizing the notion of Körner's graph entropy. We demonstrate the coding gains of fractional coloring over traditional coloring via a computation example. We conjecture that the integrality gap between fractional coloring and traditional coloring approaches the smallest b that attains the fractional chromatic number to losslessly represent the independent sets for a given characteristic graph, up to a linear scaling which is a function of the fractional chromatic number.

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arXiv2021

Transmission Delay Minimization via Joint Power Control and Caching in Wireless HetNets

A fundamental challenge in wireless heterogeneous networks (HetNets) is to effectively utilize the limited transmission and storage resources in the presence of increasing deployment density and backhaul capacity constraints. To alleviate bottlenecks and reduce resource consumption, we design optimal caching and power control algorithms for multi-hop wireless HetNets. We formulate a joint optimization framework to minimize the average transmission delay as a function of the caching variables and the signal-to-interference-plus-noise ratios (SINR) which are determined by the transmission powers, while explicitly accounting for backhaul connection costs and the power constraints. Using convex relaxation and rounding, we obtain a reduced-complexity formulation (RCF) of the joint optimization problem, which can provide a constant factor approximation to the globally optimal solution. We then solve RCF in two ways: 1) alternating optimization of the power and caching variables by leveraging biconvexity, and 2) joint optimization of power control and caching. We characterize the necessary (KKT) conditions for an optimal solution to RCF, and use strict quasi-convexity to show that the KKT points are Pareto optimal for RCF. We then devise a subgradient projection algorithm to jointly update the caching and power variables, and show that under appropriate conditions, the algorithm converges at a linear rate to the local minima of RCF, under general SINR conditions. We support our analytical findings with results from extensive numerical experiments.

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arXiv2021

Distributed Computation over MAC via Kolmogorov-Arnold Representation

Kolmogorov's representation theorem provides a framework for decomposing any arbitrary real-valued, multivariate, and continuous function into a two-layer nested superposition of a finite number of functions. The functions at these two layers, are referred to as the inner and outer functions with the key property that the design of the inner functions is independent of that of the original function of interest to be computed. This brings modularity and universality to the design of the inner function, and subsequently, a part of computation. This paper capitalizes on such modularity and universality in functional representation to propose two frameworks for distributed computation over the additive multiple access channels (MACs). In the first framework, each source encodes the inner representations and sends them over the additive MAC. Subsequently, the receiver computes the outer functions to compute the function of interest. Transmitting the values of the inner functions instead of the messages directly leads to compression gains. In the second approach, in order to further increase the compression rate, the framework aims to also bring computing the outer functions to the source sites. Specifically, each source employs a graph-coloring-based approach to perform joint functional compression of the inner and the outer functions, which may attain further compression savings over the former. These modular encoding schemes provide an exact representation in the asymptotic regime and the non-asymptotic regime. Contrasting these with the baseline model where sources directly transmit data over MAC, we observe gains. To showcase the gains of these two frameworks and their discrepancies, they are applied to a number of commonly used computations in distributed systems, e.g., computing products, $\ell_m$-norms, polynomial functions, extremum values of functions, and affine transformations.

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