arXiv subjects

Derya Malak

Publications and source records attributed to Derya Malak.

34 records · Page 2Linked to original sources

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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arXiv2021

Applications of Common Information to Computing Functions

We design a low complexity distributed compression scheme for computing arbitrary functions of sources with discrete alphabets. We use a helper-based method that extends the definition of the G{á}cs-K{ö}rner-Witsenhausen (GKW) common information to functional common information. The helper relaxes the combinatorial structure of GKW by partitioning the joint source distribution into nests imposed by the function, which ensures hierarchical cooperation between the sources for effectively distributed computing. By contrasting our approach's performance with existing efficient techniques, we demonstrate the rate savings in recovering function and source data. Permutation invariant functions are prevalent in learning and combinatorial optimization fields and most recently applied to graph neural networks. We consider the efficient compression for computing permutation invariant functions in a network with two sources and one decoder. We use a bipartite graph representation, where two disjoint sets of vertices (parts) denote the individual source graphs and the edge weights capture the joint source distribution. We compress bipartite graphs by creating connected components determined by the function's distribution, accounting for the edge symmetries, and eliminating the low probability edges. We separately encode those edges and send them as refinements. Our approach can substitute high complexity joint decoding techniques and inform neural networks to reduce the computing time and reduce complexity.

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arXiv2021

Spatial Concentration of Caching in Wireless Heterogeneous Networks

We propose a decentralized caching policy for wireless heterogeneous networks that makes content placement decisions based on pairwise interactions between cache nodes. We call our proposed scheme γ-exclusion cache placement (GEC), where a parameter γ controls an exclusion radius that discourages nearby caches from storing redundant content. GEC takes into account item popularity and the nodes' caching priorities and leverages negative dependence to relax the classic 0-1 knapsack problem to yield spatially balanced sampling across caches. We show that GEC guarantees a better concentration (reduced variance) of the required cache storage size than the state of the art, and that the cache size constraints can be satisfied with high probability. Given a cache hit probability target, we compare the 95\% confidence intervals of the required cache sizes for three caching schemes: (i) independent placement, (ii) hard exclusion caching (HEC), and (iii) the proposed GEC approach. For uniform spatial traffic, we demonstrate that GEC provides approximately a 3x and 2x reduction in required cache size over (i) and (ii), respectively. For non-uniform spatial traffic based on realistic peak-hour variations in urban scenarios, the gains are even greater.

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arXiv2020

Function Load Balancing over Networks

Using networks as a means of computing can reduce the communication flow or the total number of bits transmitted over the networks. In this paper, we propose to distribute the computation load in stationary networks, and formulate a flow-based delay minimization problem that jointly captures the aspects of communications and computation. We exploit the distributed compression scheme of Slepian-Wolf that is applicable under any protocol information where nodes can do compression independently using different codebooks. We introduce the notion of entropic surjectivity as a measure to determine how sparse the function is and to understand the limits of functional compression for computation. We leverage Little's Law for stationary systems to provide a connection between surjectivity and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network without putting any assumptions on the topology. Our results suggest that to effectively compute different function classes that have different entropic surjectivities, the networks can be re-structured with the transition probabilities being tailored for functions, i.e., task-based link reservations, which can enable mixing versus separately processing of a diverse function classes. They also imply that most of the available resources are reserved for computing low complexity functions versus fewer resources for processing of high complexity ones. We numerically evaluate our technique for search, MapReduce, and classification functions, and infer how sensitive the processing factor for each computation task to the entropic surjectivity is.

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arXiv2020

How to Distribute Computation in Networks

In network function computation is as a means to reduce the required communication flow in terms of number of bits transmitted per source symbol. However, the rate region for the function computation problem in general topologies is an open problem, and has only been considered under certain restrictive assumptions (e.g. tree networks, linear functions, etc.). In this paper, we propose a new perspective for distributing computation, and formulate a flow-based delay cost minimization problem that jointly captures the costs of communications and computation. We introduce the notion of entropic surjectivity as a measure to determine how sparse the function is and to understand the limits of computation. Exploiting Little's law for stationary systems, we provide a connection between this new notion and the computation processing factor that reflects the proportion of flow that requires communications. This connection gives us an understanding of how much a node (in isolation) should compute to communicate the desired function within the network without putting any assumptions on the topology. Our analysis characterizes the functions only via their entropic surjectivity, and provides insight into how to distribute computation. We numerically test our technique for search, MapReduce, and classification tasks, and infer for each task how sensitive the processing factor to the entropic surjectivity is.

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arXiv2019

Adaptive Causal Network Coding with Feedback

We propose a novel adaptive and causal random linear network coding (AC-RLNC) algorithm with forward error correction (FEC) for a point-to-point communication channel with delayed feedback. AC-RLNC is adaptive to the channel condition, that the algorithm estimates, and is causal, as coding depends on the particular erasure realizations, as reflected in the feedback acknowledgments. Specifically, the proposed model can learn the erasure pattern of the channel via feedback acknowledgments, and adaptively adjust its retransmission rates using a priori and posteriori algorithms. By those adjustments, AC-RLNC achieves the desired delay and throughput, and enables transmission with zero error probability. We upper bound the throughput and the mean and maximum in order delivery delay of AC-RLNC, and prove that for the point to point communication channel in the non-asymptotic regime the proposed code may achieve more than 90% of the channel capacity. To upper bound the throughput we utilize the minimum Bhattacharyya distance for the AC-RLNC code. We validate those results via simulations. We contrast the performance of AC-RLNC with the one of selective repeat (SR)-ARQ, which is causal but not adaptive, and is a posteriori. Via a study on experimentally obtained commercial traces, we demonstrate that a protocol based on AC-RLNC can, vis-`a-vis SR-ARQ, double the throughput gains, and triple the gain in terms of mean in order delivery delay when the channel is bursty. Furthermore, the difference between the maximum and mean in order delivery delay is much smaller than that of SR-ARQ. Closing the delay gap along with boosting the throughput is very promising for enabling ultra-reliable low-latency communications (URLLC) applications.

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arXiv2019

Tiny Codes for Guaranteeable Delay

Future 5G systems will need to support ultra-reliable low-latency communications scenarios. From a latency-reliability viewpoint, it is inefficient to rely on average utility-based system design. Therefore, we introduce the notion of guaranteeable delay which is the average delay plus three standard deviations of the mean. We investigate the trade-off between guaranteeable delay and throughput for point-to-point wireless erasure links with unreliable and delayed feedback, by bringing together signal flow techniques to the area of coding. We use tiny codes, i.e. sliding window by coding with just 2 packets, and design three variations of selective-repeat ARQ protocols, by building on the baseline scheme, i.e. uncoded ARQ, developed by Ausavapattanakun and Nosratinia: (i) Hybrid ARQ with soft combining at the receiver; (ii) cumulative feedback-based ARQ without rate adaptation; and (iii) Coded ARQ with rate adaptation based on the cumulative feedback. Contrasting the performance of these protocols with uncoded ARQ, we demonstrate that HARQ performs only slightly better, cumulative feedback-based ARQ does not provide significant throughput while it has better average delay, and Coded ARQ can provide gains up to about 40% in terms of throughput. Coded ARQ also provides delay guarantees, and is robust to various challenges such as imperfect and delayed feedback, burst erasures, and round-trip time fluctuations. This feature may be preferable for meeting the strict end-to-end latency and reliability requirements of future use cases of ultra-reliable low-latency communications in 5G, such as mission-critical communications and industrial control for critical control messaging.

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arXiv2019

Spatial Soft-Core Caching

We propose a decentralized spatial soft-core cache placement (SSCC) policy for wireless networks. SSCC yields a spatially balanced sampling via negative dependence across caches, and can be tuned to satisfy cache size constraints with high probability. Given a desired cache hit probability, we compare the 95% confidence intervals of the required cache sizes for independent placement, hard-core placement and SSCC policies. We demonstrate that in terms of the required cache storage size, SSCC can provide up to more than 180% and 100% gains with respect to the independent and hard-core placement policies, respectively. SSCC can be used to enable proximity-based applications such as device-to-device communications and peer-to-peer networking as it promotes the item diversity and reciprocation among the nodes.

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arXiv2018

ARQ with Cumulative Feedback to Compensate for Burst Errors

We propose a cumulative feedback-based ARQ (CF ARQ) protocol for a sliding window of size 2 over packet erasure channels with unreliable feedback. We exploit a matrix signal-flow graph approach to analyze probability-generating functions of transmission and delay times. Contrasting its performance with that of the uncoded baseline scheme for ARQ, developed by Ausavapattanakun and Nosratinia, we demonstrate that CF ARQ can provide significantly less average delay under bursty feedback, and gains up to about 20% in terms of throughput. We also outline the benefits of CF ARQ under burst errors and asymmetric channel conditions. The protocol is more predictable across statistics, hence is more stable. This can help design robust systems when feedback is unreliable. This feature may be preferable for meeting the strict end-to-end latency and reliability requirements of future use cases of ultra-reliable low-latency communications in 5G, such as mission-critical communications and industrial control for critical control messaging.

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arXiv2018

Throughput Maximization for Delay-Sensitive Random Access Communication

Future 5G cellular networks supporting ultra-reliable, low-latency communications (URLLC) could employ random access communication to reduce the overhead compared to scheduled access techniques used in 4G networks. We consider a wireless communication system where multiple devices transmit payloads of a given fixed size in a random access fashion over shared radio resources to a common receiver. We allow retransmissions and assume Chase combining at the receiver. The radio resources are partitioned in the time and frequency dimensions, and we determine the optimal partition granularity to maximize throughput, subject to given constraints on latency and outage. In the regime of high and low signal-to-noise ratio (SNR), we derive explicit expressions for the granularity and throughput, first using a Shannon capacity approximation and then using finite block length analysis. Numerical results show that the throughput scaling results are applicable over a range of SNRs. The proposed analytical framework can provide insights for resource allocation strategies in general random access systems and in specific 5G use cases for massive URLLC uplink access.

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arXiv2018

Analysis of Coded Selective-Repeat ARQ via Matrix Signal-Flow Graphs

We propose two schemes for selective-repeat ARQ protocols over packet erasure channels with unreliable feedback: (i) a hybrid ARQ protocol with soft combining at the receiver, and (ii) a coded ARQ protocol, by building on the uncoded baseline scheme for ARQ, developed by Ausavapattanakun and Nosratinia. Our method leverages discrete-time queuing and coding theory to analyze the performance of the proposed data transmission methods. We incorporate forward error-correction to reduce in-order delivery delay, and exploit a matrix signal-flow graph approach to analyze the throughput and delay of the protocols. We demonstrate and contrast the performance of the coded protocols with that of the uncoded scheme, illustrating the benefits of coded transmissions.

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arXiv2017

A Distributed Auction Policy for User Association in Device-to-Device Caching Networks

We propose a distributed bidding-aided Matern carrier sense multiple access (CSMA) policy for device-to-device (D2D) content distribution. The network is composed of D2D receivers and potential D2D transmitters, i.e., transmitters are turned on or off by the scheduling algorithm. Each D2D receiver determines the value of its request, by bidding on the set of potential transmitters in its communication range. Given a medium access probability, a fraction of the potential transmitters are jointly scheduled, i.e., turned on, determined jointly by the auction policy and the power control scheme. The bidding-aided scheduling algorithm exploits (i) the local demand distribution, (ii) spatial distribution of D2D node locations, and (iii) the cache configurations of the potential transmitters. We contrast the performance of the bidding-aided CSMA policy with other well-known CSMA schemes that do not take into account (i)-(iii), demonstrate that our algorithm achieves a higher spectral efficiency in terms of the number of bits transmitted per unit time per unit bandwidth per user. The gain becomes even more visible under randomized configurations and requests rather than more skewed placement configurations and deterministic demand distributions.

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arXiv2017

Spatially Correlated Content Caching for Device-to-Device Communications

We study optimal geographic content placement for device-to-device (D2D) networks in which each file's popularity follows the Zipf distribution. The locations of the D2D users (caches) are modeled by a Poisson point process (PPP) and have limited communication range and finite storage. Inspired by the Matérn hard-core (type II) point process that captures pairwise interactions between nodes, we devise a novel spatially correlated caching strategy called {\em hard-core placement} (HCP) such that the D2D nodes caching the same file are never closer to each other than the {\em exclusion radius}. The exclusion radius plays the role of a substitute for caching probability. We derive and optimize the exclusion radii to maximize the {\em hit probability}, which is the probability that a given D2D node can find a desired file at another node's cache within its communication range. Contrasting it with independent content placement, which is used in most prior work, our HCP strategy often yields a significantly higher cache hit probability. We further demonstrate that the HCP strategy is effective for small cache sizes and a small communication radius, which are likely conditions for D2D.

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arXiv2016

Optimizing The Spatial Content Caching Distribution for Device-to-Device Communications

We study the optimal geographic content placement problem for device-to-device (D2D) networks in which the content popularity follows the Zipf law. We consider a D2D caching model where the locations of the D2D users (caches) are modeled by a Poisson point process (PPP) and have limited communication range and finite storage. Unlike most related work which assumes independent placement of content, and does not capture the locations of the users, we model the spatial properties of the network including spatial correlation in terms of the cached content. We propose two novel spatial correlation models, the exchangeable content model and a Matérn (MHC) content placement model, and analyze and optimize the \emph{hit probability}, which is the probability of a given D2D node finding a desired file at another node within its communication range. We contrast these results to the independent placement model, and show that exchangeable placement performs worse. On the other hand, MHC placement yields a higher cache hit probability than independent placement for small cache sizes.

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arXiv2016

Optimizing Content Caching to Maximize the Density of Successful Receptions in Device-to-Device Networking

Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized opportunistic short-range communication. For D2D to be useful, mobile nodes must possess content that other mobiles want. Thus, intelligent caching techniques are essential for D2D. In this paper we use results from stochastic geometry to derive the probability of successful content delivery in the presence of interference and noise. We employ a general transmission strategy where multiple files are cached at the users and different files can be transmitted simultaneously throughout the network. We then formulate an optimization problem, and find the caching distribution that maximizes the density of successful receptions (DSR) under a simple transmission strategy where a single file is transmitted at a time throughout the network. We model file requests by a Zipf distribution with exponent $γ_r$, which results in an optimal caching distribution that is also a Zipf distribution with exponent $γ_c$, which is related to $γ_r$ through a simple expression involving the path loss exponent. We solve the optimal content placement problem for more general demand profiles under Rayleigh, Ricean and Nakagami small-scale fading distributions. Our results suggest that it is required to flatten the request distribution to optimize the caching performance. We also develop strategies to optimize content caching for the more general case with multiple files, and bound the DSR for that scenario.

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arXiv2015

Optimizing Data Aggregation for Uplink Machine-to-Machine Communication Networks

Machine-to-machine (M2M) communication's severe power limitations challenge the interconnectivity, access management, and reliable communication of data. In densely deployed M2M networks, controlling and aggregating the generated data is critical. We propose an energy efficient data aggregation scheme for a hierarchical M2M network. We develop a coverage probability-based optimal data aggregation scheme for M2M devices to minimize the average total energy expenditure per unit area per unit time or simply the {\em energy density} of an M2M communication network. Our analysis exposes the key tradeoffs between the energy density of the M2M network and the coverage characteristics for successive and parallel transmission schemes that can be either half-duplex or full-duplex. Comparing the rate and energy performances of the transmission models, we observe that successive mode and half-duplex parallel mode have better coverage characteristics compared to full-duplex parallel scheme. Simulation results show that the uplink coverage characteristics dominate the trend of the energy consumption for both successive and parallel schemes.

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