arXiv subjects

Parastoo Sadeghi

Publications and source records attributed to Parastoo Sadeghi.

At least 73 records · Page 4Linked to original sources

arXiv2020

Independent User Partition Multicast Scheme for the Groupcast Index Coding Problem

The groupcast index coding (GIC) problem is a generalization of the index coding problem, where one packet can be demanded by multiple users. In this paper, we propose a new coding scheme called independent user partition multicast (IUPM) for the GIC problem. The novelty of this scheme compared to the user partition multicast (UPM) (Shanmugam \textit{et al.}, 2015) is in removing redundancies in the UPM solution by eliminating the linearly dependent coded packets. We also prove that the UPM scheme subsumes the packet partition multicast (PPM) scheme (Tehrani \textit{et al.}, 2012). Hence, the IUPM scheme is a generalization of both PPM and UPM schemes. Furthermore, inspired by jointly considering users and packets, we modify the approximation partition multicast (CAPM) scheme (Unal and Wagner, 2016) to achieve a new polynomial-time algorithm for solving the general GIC problem. We characterize a class of GIC problems with $\frac{k(k-1)}{2}$ packets, for any integer $k\geq 2$, for which the IUPM scheme is optimal. We also prove that for this class, the broadcast rate of the proposed new heuristic algorithm is $k$, while the broadcast rate of the CAPM scheme is $\mathcal{O}(k^2)$.

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arXiv2019

Part II: A Practical Approach for Successive Omniscience

In Part I, we studied the communication for omniscience (CO) problem and proposed a parametric (PAR) algorithm to determine the minimum sum-rate at which a set of users indexed by a finite set $V$ attain omniscience. The omniscience in CO refers to the status that each user in $V$ recovers the observations of a multiple random source. It is called the global omniscience in this paper in contrast to the study of the successive omniscience (SO), where the local omniscience is attained subsequently in user subsets. By inputting a lower bound on the minimum sum-rate for CO, we apply the PAR algorithm to search a complimentary subset $X_* \subsetneq V$ such that if the local omniscience in $X_*$ is reached first, the global omniscience whereafter can still be attained with the minimum sum-rate. We further utilize the outputs of the PAR algorithm to outline a multi-stage SO approach that is characterized by $K \leq |V| - 1$ complimentary subsets $X_*^{(k)}, \forall k \in \{1,\dotsc,K\}$ forming a nesting sequence $X_*^{(1)} \subsetneq \dotsc \subsetneq X_*^{(K)} = V$. Starting from stage $k = 1$, the local omniscience in $X_*^{(k)}$ is attained at each stage $k$ until the final global omniscience in $X_*^{(K)} = V$. A $|X_*{(k)}|$-dimensional local omniscience achievable rate vector is also derived for each stage $k$ designating individual users transmitting rates. The sum-rate of this rate vector in the last stage $K$ coincides with the minimized sum-rate for the global omniscience.

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arXiv2019

Improved Lower Bounds for Pliable Index Coding using Absent Receivers

This paper studies pliable index coding, in which a sender broadcasts information to multiple receivers through a shared broadcast medium, and the receivers each have some message a priori and want any message they do not have. An approach, based on receivers that are absent from the problem, was previously proposed to find lower bounds on the optimal broadcast rate. In this paper, we introduce new techniques to obtained better lower bounds, and derive the optimal broadcast rates for new classes of the problems, including all problems with up to four absent receivers.

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arXiv2019

Multirate Packet Delivery In Heterogeneous Broadcast Networks

In this paper, we study the problem of multirate packet delivery in heterogeneous packet erasure broadcast networks. The technical challenge is to enable users receive packets at different rates, as dictated by the quality of their individual channel. We present a new analytical framework for characterizing the delivery rate and delivery delay performance of a previously proposed non-block-based network coding scheme in the literature. This scheme was studied in homogeneous network settings. We show for the first time, via new theoretical analysis and simulations that it can actually achieve multirate packet delivery. Using acknowledgments from each user, we show that the user with the highest link capacity achieves the maximum possible throughput. Also, a non-zero packet delivery rate is possible for other users, and the delivery rate depends on the difference between the packet arrival rate at the sender and the link capacity of each user. The accuracy of our analytical framework is confirmed by comparing the results with simulations for different settings of packet arrival rate at the sender and link capacities.

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arXiv2019

Generalized Alignment Chain: Improved Converse Results for Index Coding

In this paper, we study the information-theoretic converse for the index coding problem. We generalize the definition for the alignment chain, introduced by Maleki et al., to capture more flexible relations among interfering messages at each receiver. Based on this, we derive improved converse results for the single-server index coding problem. Compared to the maximum acyclic induced subgraph (MAIS) bound, the new bounds are always as tight and can strictly outperform the MAIS bound. They can also be useful for large problems, where the generally tighter polymatroidal bound is computationally impractical. We then extend these new bounds to the multi-server index coding problem. We also present a separate, but related result where we identify a smaller single-server index coding instance, compared to those identified in the literature, for which non-Shannon-type inequalities are necessary to give a tighter converse.

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arXiv2019

Improving Computational Efficiency of Communication for Omniscience and Successive Omniscience

For a group of users in $V$ where everyone observes a component of a discrete multiple random source, the process that users exchange data so as to reach omniscience, the state where everyone recovers the entire source, is called communication for omniscience (CO). We first consider how to improve the existing complexity $O(|V|^2 \cdot \text{SFM}(|V|)$ of minimizing the sum of communication rates in CO, where $\text{SFM}(|V|)$ denotes the complexity of minimizing a submodular function. We reveal some structured property in an existing coordinate saturation algorithm: the resulting rate vector and the corresponding partition of $V$ are segmented in $α$, the estimation of the minimum sum-rate. A parametric (PAR) algorithm is then proposed where, instead of a particular $α$, we search the critical points that fully determine the segmented variables for all $α$ so that they converge to the solution to the minimum sum-rate problem and the overall complexity reduces to $O(|V| \cdot \text{SFM}(|V|))$. For the successive omniscience (SO), we consider how to attain local omniscience in some complimentary user subset so that the overall sum-rate for the global omniscience still remains minimum. While the existing algorithm only determines a complimentary user subset in $O(|V| \cdot \text{SFM}(|V|))$ time, we show that, if a lower bound on the minimum sum-rate is applied to the segmented variables in the PAR algorithm, not only a complimentary subset, but also an optimal rate vector for attaining the local omniscience in it are returned in $O(|V| \cdot \text{SFM}(|V|))$ time.

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arXiv2019

A Submodularity-based Agglomerative Clustering Algorithm for the Privacy Funnel

For the privacy funnel (PF) problem, we propose an efficient iterative agglomerative clustering algorithm based on the minimization of the difference of submodular functions (IAC-MDSF). For a data curator that wants to share the data $X$ correlated with the sensitive information $S$, the PF problem is to generate the sanitized data $\hat{X}$ that maintains a specified utility/fidelity threshold on $I(X; \hat{X})$ while minimizing the privacy leakage $I(S; \hat{X})$. Our IAC-MDSF algorithm starts with the original alphabet $\hat{\mathcal{X}} := \mathcal{X}$ and iteratively merges the elements in the current alphabet $\hat{\mathcal{X}}$ that minimizes the Lagrangian function $ I(S;\hat{X}) - λI(X;\hat{X}) $. We prove that the best merge in each iteration of IAC-MDSF can be searched efficiently over all subsets of $\hat{\mathcal{X}}$ by the existing MDSF algorithms. We show that the IAC-MDSF algorithm also applies to the information bottleneck (IB), a dual problem to PF. By varying the value of the Lagrangian multiplier $λ$, we obtain the experimental results on a heart disease data set in terms of the Pareto frontier: $ I(S;\hat{X})$ vs. $- I(X;\hat{X})$. We show that our IAC-MDSF algorithm outperforms the existing iterative pairwise merge approaches for both PF and IB and is computationally much less complex.

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arXiv2019

Attaining Fairness in Communication for Omniscience

This paper studies how to attain fairness in communication for omniscience, where a set of users exchange their observations of a discrete multiple random source to attain omniscience---the state that all users recover the entire source. The optimal rate region containing all source coding rate vectors that achieve the omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game. Two game-theoretic fairness solutions are studied: the Shapley value and the egalitarian solution. It is shown that the Shapley value assigns each user the source coding rate measured by his/her remaining information of the multiple source given the common randomness that is shared by all users, while the egalitarian solution simply distributes the rates as evenly as possible in the core. To avoid the exponentially growing complexity of obtaining the Shapley value, a polynomial-time approximation method is proposed by utilizing the fact that the Shapley value is the mean value over all extreme points in the core. In addition, a steepest descent algorithm is proposed which converges in polynomial time to the fractional egalitarian solution in the core that can be implemented by network coding schemes. Finally, it is shown that the game can be decomposed into subgames so that both the Shapley value and the egalitarian solution can be obtained within each subgame in a distributed manner with reduced complexity.

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arXiv2018

On the Capacity Region for Secure Index Coding

We study the index coding problem in the presence of an eavesdropper, where the aim is to communicate without allowing the eavesdropper to learn any single message aside from the messages it may already know as side information. We establish an outer bound on the underlying secure capacity region of the index coding problem, which includes polymatroidal and security constraints, as well as the set of additional decoding constraints for legitimate receivers. We then propose a secure variant of the composite coding scheme, which yields an inner bound on the secure capacity region of the index coding problem. For the achievability of secure composite coding, a secret key with vanishingly small rate may be needed to ensure that each legitimate receiver who wants the same message as the eavesdropper, knows at least two more messages than the eavesdropper. For all securely feasible index coding problems with four or fewer messages, our numerical results establish the secure index coding capacity region.

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arXiv2018

Fairness in Multiterminal Data Compression: A Splitting Method for The Egalitarian Solution

This paper proposes a novel splitting (SPLIT) algorithm to achieve fairness in the multiterminal lossless data compression problem. It finds the egalitarian solution in the Slepian-Wolf region and completes in strongly polynomial time. We show that the SPLIT algorithm adaptively updates the source coding rates to the optimal solution, while recursively splitting the terminal set, enabling parallel and distributed computation. The result of an experiment demonstrates a significant reduction in computation time by the parallel implementation when the number of terminals becomes large. The achieved egalitarian solution is also shown to be superior to the Shapley value in distributed networks, e.g., wireless sensor networks, in that it best balances the nodes' energy consumption and is far less computationally complex to obtain.

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arXiv2018

Distributed Data Compression in Sensor Clusters: A Maximum Independent Flow Approach

Let a cluster (network) of sensors be connected by the communication links, each link having a capacity upper bound. Each sensor observes a discrete random variable in private and one sensor serves as a cluster header or sink. Here, we formulate the problem of how to let the sensors encode their observations such that the direction of compressed data is a feasible flow towards the sink. We demonstrate that this problem can be solved by an existing maximum independent flow (MIF) algorithm in polynomial time. Further, we reveal that this algorithm in fact determines an optimal solution by recursively pushing the remaining randomness in the sources via unsaturated communication links towards the sink. We then show that the MIF algorithm can be implemented in a distributed manner. For those networks with integral communication capacities, we propose an integral MIF algorithm which completes much faster than MIF. Finally, we point out that the nature of the data compression problem in a sensor cluster is to seek the maximum independent information flow in the intersection of two submodular polyhedra, which can be further utilized to improve the MIF algorithm in the future.

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arXiv2018

Fairness in Multiterminal Data Compression: Decomposition of Shapley Value

We consider the problem of how to determine a fair source coding rate allocation method for the lossless data compression problem in multiterminal networks, e.g, the wireless sensor network where there are a large number of sources to be encoded. We model this problem by a game-theoretic approach and present a decomposition method for obtaining the Shapley value, a fair source coding rate vector in the Slepian-Wolf achievable region. We formulate a coalitional game model where the entropy function quantifies the cost incurred due to the source coding rates in each coalition. In the typical case for which the game is decomposable, we show that the Shapley value can be obtained separately for each subgame. The complexity of this decomposition method is determined by the maximum size of subgames, which is strictly smaller than the total number of sources and contributes to a considerable reduction in computational complexity. Experiments demonstrate large complexity reduction when the number of sources becomes large.

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arXiv2018

On the Packet Decoding Delay of Linear Network Coded Wireless Broadcast

We apply linear network coding (LNC) to broadcast a block of data packets from one sender to a set of receivers via lossy wireless channels, assuming each receiver already possesses a subset of these packets and wants the rest. We aim to characterize the average packet decoding delay (APDD), which reflects how soon each individual data packet can be decoded by each receiver on average, and to minimize it while achieving optimal throughput. To this end, we first derive closed-form lower bounds on the expected APDD of all LNC techniques under random packet erasures. We then prove that these bounds are NP-hard to achieve and, thus, that APDD minimization is an NP-hard problem. We then study the performance of some existing LNC techniques, including random linear network coding (RLNC) and instantly decodable network coding (IDNC). We proved that all throughput-optimal LNC techniques can approximate the minimum expected APDD with a ratio between 4/3 and 2. In particular, the ratio of RLNC is exactly 2. We then prove that all IDNC techniques are only heuristics in terms of throughput optimization and {cannot guarantee an APDD approximation ratio for at least a subset of the receivers}. Finally, we propose hyper-graphic linear network coding (HLNC), a novel throughput-optimal and APDD-approximating LNC technique based on a hypergraph model of receivers' packet reception state. We implement it under different availability of receiver feedback, and numerically compare its performance with RLNC and a heuristic general IDNC technique. The results show that the APDD performance of HLNC is better under all tested system settings, even if receiver feedback is only collected intermittently.

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arXiv2017

A Practical Approach for Successive Omniscience

The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value, of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO.

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arXiv2017

On the Capacity for Distributed Index Coding

The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized (single-server) index coding problem, which is then merged with fractional partitioning of servers to yield a new coding scheme for distributed index coding. New outer bounds on the capacity region are also established. For 213 out of 218 non-isomorphic distributed index coding problems with four messages the achievable sum-rate of the proposed distributed composite coding scheme matches the outer bound, thus establishing the sum-capacity for these problems.

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arXiv2017

Approximating Throughput and Packet Decoding Delay in Linear Network Coded Wireless Broadcast

In this paper, we study a wireless packet broadcast system that uses linear network coding (LNC) to help receivers recover data packets that are missing due to packet erasures. We study two intertwined performance metrics, namely throughput and average packet decoding delay (APDD) and establish strong/weak approximation relations based on whether the approximation holds for the performance of every receiver (strong) or for the average performance across all receivers (weak). We prove an equivalence between strong throughput approximation and strong APDD approximation. We prove that throughput-optimal LNC techniques can strongly approximate APDD, and partition-based LNC techniques may weakly approximate throughput. We also prove that memoryless LNC techniques, including instantly decodable network coding techniques, are not strong throughput and APDD approximation nor weak throughput approximation techniques.

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arXiv2016

User Load Analysis and Pilot Sequence Design for Multi-Cell Massive MIMO Networks

We propose a novel algorithm to design user load-achieving pilot sequences that mitigate pilot contamination in multi-cell massive multiple-input multiple-output (MIMO) networks. To this end, we first derive expressions for the user load and the load region of the network considering both small-scale and large-scale propagation effects. We then develop the pilot sequence algorithm for multi-cell massive MIMO networks as per the rules of generalized Welch bound equality design. Notably, we find that our algorithm and the corresponding downlink power allocation ensure that the user load is achieved when the signal-to-interference-plus-noise ratio (SINR) requirements for the users lie within the load region. Furthermore, we demonstrate the performance advantage of our proposed design relative to the existing designs, in terms of a larger load region and a higher maximum permitted SINR. Finally, we show that our proposed design can satisfy the pre-defined SINR requirements for users with a finite number of antennas at the base station (BS), while the existing designs cannot satisfy the same requirements even with an infinite number of antennas at the BS.

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arXiv2016

Multi-Cell Multiuser Massive MIMO Networks: User Capacity Analysis and Pilot Design

We propose a novel pilot sequence design to mitigate pilot contamination in multi-cell multiuser massive multiple-input multiple-output networks. Our proposed design generates pilot sequences in the multi-cell network and devises power allocation at base stations (BSs) for downlink transmission. The pilot sequences together with the power allocation ensure that the user capacity of the network is achieved and the pre-defined signal-to-interference-plus-noise ratio (SINR) requirements of all users are met. To realize our design, we first derive new closed-form expressions for the user capacity and the user capacity region. Built upon these expressions, we then develop a new algorithm to obtain the required pilot sequences and power allocation. We further determine the minimum number of antennas required at BSs to achieve certain SINR requirements of all users. Numerical results are presented to corroborate our analysis and to examine the impact of key parameters, such as the pilot sequence length and the total number of users, on the network performance. A pivotal conclusion is reached that our design achieves a larger user capacity region than the existing designs and needs less antennas at the BS to fulfill the pre-defined SINR requirements of all users in the network than the existing designs.

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