arXiv subjects

Soheil Mohajer

Publications and source records attributed to Soheil Mohajer.

At least 37 records · Page 2Linked to original sources

arXiv2019

Determinant Codes with Helper-Independent Repair for Single and Multiple Failures

Determinant codes are a class of exact-repair regenerating codes for distributed storage systems with parameters (n, k = d, d). These codes cover the entire trade-off between per-node storage and repair-bandwidth. In an earlier work of the authors, the repair data of the determinant code sent by a helper node to repair a failed node depends on the identity of the other helper nodes participating in the process, which is practically undesired. In this work, a new repair mechanism is proposed for determinant codes, which relaxes this dependency, while preserving all other properties of the code. Moreover, it is shown that the determinant codes are capable of repairing multiple failures, with a per-node repair-bandwidth which scales sub-linearly with the number of failures.

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arXiv2018

Cache Aided Communications with Multiple Antennas at Finite SNR

We study the problem of cache-aided communication for cellular networks with multi-user and multiple antennas at finite signal-to-noise ratio. Users are assumed to have non-symmetric links, modeled by wideband fading channels. We show that the problem can be formulated as a linear program, whose solution provides a joint cache allocation along with pre-fetching and fetching schemes that minimize the duration of the communication in the delivery phase. The suggested scheme uses zero-forcing and cached interference subtraction and hence allow each user to be served at the rate of its own channel. Thus, this scheme is better than the previously published schemes that are compromised by the poorest user in the communication group. We also consider a special case of the parameters for which we can derive a closed form solution and formulate the optimal power, rate and cache optimization. This special case shows that the gain of MIMO coded caching goes beyond the throughput. In particular, it is shown that in this case, the cache is used to balance the users such that fairness and throughput are no longer contradicting. More specifically, in this case, strict fairness is achieved jointly with maximizing the network throughput.

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arXiv2017

Product Matrix MSR Codes with Bandwidth Adaptive Exact Repair

In a distributed storage systems (DSS) with $k$ systematic nodes, robustness against node failure is commonly provided by storing redundancy in a number of other nodes and performing repair mechanism to reproduce the content of the failed nodes. Efficiency is then achieved by minimizing the storage overhead and the amount of data transmission required for data reconstruction and repair, provided by coding solutions such as regenerating codes [1]. Common explicit regenerating code constructions enable efficient repair through accessing a predefined number, $d$, of arbitrary chosen available nodes, namely helpers. In practice, however, the state of the system dynamically changes based on the request load, the link traffic, etc., and the parameters which optimize system's performance vary accordingly. It is then desirable to have coding schemes which are able to operate optimally under a range of different parameters simultaneously. Specifically, adaptivity in the number of helper nodes for repair is of interest. While robustness requires capability of performing repair with small number of helpers, it is desirable to use as many helpers as available to reduce the transmission delay and total repair traffic. In this work we focus on the minimum storage regenerating (MSR) codes, where each node is supposed to store $α$ information units, and the source data of size $kα$ could be recovered from any arbitrary set of $k$ nodes. We introduce a class MSR codes that realize optimal repair bandwidth simultaneously with a set of different choices for the number of helpers, namely $D=\{d_{1}, \cdots, d_δ\}$. Our coding scheme follows the Product Matrix (PM) framework introduced in [2], and could be considered as a generalization of the PM MSR code presented in [2], such that any $d_{i} = (i+1)(k-1)$ helpers can perform an optimal repair. ...

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arXiv2017

Product Matrix Minimum Storage Regenerating Codes with Flexible Number of Helpers

In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the number of helper nodes participating in a repair process, are predetermined. However, depending on the state of the system and network traffic, it is desirable to adapt such parameters accordingly in order to minimize the cost of repair. In this work a class of regenerating codes with minimum storage is introduced that can simultaneously operate at the optimal repair bandwidth, for a wide range of exact repair mechanisms, based on different number of helper nodes.

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arXiv2017

Bandwidth Adaptive & Error Resilient MBR Exact Repair Regenerating Codes

Regenerating codes are efficient methods for distributed storage in storage networks, where node failures are common. They guarantee low cost data reconstruction and repair through accessing only a predefined number of arbitrarily chosen storage nodes in the network. In this work we consider two simultaneous extensions to the original regenerating codes framework introduced in [1]; i) both data reconstruction and repair are resilient to the presence of a certain number of erroneous nodes in the network and ii) the number of helper nodes in every repair is not fixed, but is a flexible parameter that can be selected during the runtime. We study the fundamental limits of required total repair bandwidth and provide an upper bound for the storage capacity of these codes under these assumptions. We then focus on the minimum repair bandwidth (MBR) case and derive the exact storage capacity by presenting explicit coding schemes with exact repair, which achieve the upper bound of the storage capacity in the considered setup. To this end, we first provide a more natural extension of the well-known Product Matrix (PM) MBR codes [2], modified to provide flexibility in the choice of number of helpers in each repair, and simultaneously be robust to erroneous nodes in the network. This is achieved by proving the non-singularity of family of matrices in large enough finite fields. We next provide another extension of the PM codes, based on novel repair schemes which enable flexibility in the number of helpers and robustness against erroneous nodes without any extra cost in field size compared to the original PM codes.

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arXiv2016

Role of a Relay in Bursty Multiple Access Channels

We investigate the role of a relay in multiple access channels (MACs) with bursty user traffic, where intermittent data traffic restricts the users to bursty transmissions. As our main result, we characterize the degrees of freedom (DoF) region of a $K$-user bursty multi-input multi-output (MIMO) Gaussian MAC with a relay, where Bernoulli random states are introduced to govern bursty user transmissions. To that end, we extend the noisy network coding scheme to achieve the cut-set bound. Our main contribution is in exploring the role of a relay from various perspectives. First, we show that a relay can provide a DoF gain in bursty channels, unlike in conventional non-bursty channels. Interestingly, we find that the relaying gain can scale with additional antennas at the relay to some extent. Moreover, observing that a relay can help achieve collision-free performances, we establish the necessary and sufficient condition for attaining collision-free DoF. Lastly, we consider scenarios in which some physical perturbation shared around the users may generate data traffic simultaneously, causing transmission patterns across them to be correlated. We demonstrate that for most cases in such scenarios, the relaying gain is greater when the users' transmission patterns are more correlated, hence when more severe collisions take place. Our results have practical implications in various scenarios of wireless networks such as device-to-device systems and random media access control protocols.

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arXiv2015

A Probabilistic Approach Towards Exact-Repair Regeneration Codes

Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact- repair problem, the achievable points of (α,β) tradeoff match with the outer bound only for minimum storage regenerating (MSR), minimum bandwidth regenerating (MBR), and some specific values of n, k, and d. Such tradeoff is characterized in this work for general (n, k, k), (i.e., k = d) for some range of per-node storage (α) and repair-bandwidth (β). Rather than explicit code construction, achievability of these tradeoff points is shown by proving existence of exact-repair regeneration codes for any (n,k,k). More precisely, it is shown that an (n, k, k) system can be extended by adding a new node, which is randomly picked from some ensemble, and it is proved that, with high probability, the existing nodes together with the newly added one maintain properties of exact-repair regeneration codes. The new achievable region improves upon the existing code constructions. In particular, this result provides a complete tradeoff characterization for an (n,3,3) distributed storage system for any value of n.

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arXiv2012

On the Feedback Capacity of the Fully Connected $K$-User Interference Channel

The symmetric K user interference channel with fully connected topology is considered, in which (a) each receiver suffers interference from all other (K-1) transmitters, and (b) each transmitter has causal and noiseless feedback from its respective receiver. The number of generalized degrees of freedom (GDoF) is characterized in terms of α, where the interference-to-noise ratio (INR) is given by INR=SNR^α. It is shown that the per-user GDoF of this network is the same as that of the 2-user interference channel with feedback, except for α=1, for which existence of feedback does not help in terms of GDoF. The coding scheme proposed for this network, termed cooperative interference alignment, is based on two key ingredients, namely, interference alignment and interference decoding. Moreover, an approximate characterization is provided for the symmetric feedback capacity of the network, when the SNR and INR are far apart from each other.

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arXiv2012

On the Symmetric Feedback Capacity of the K-user Cyclic Z-Interference Channel

The K-user cyclic Z-interference channel models a situation in which the kth transmitter causes interference only to the (k-1)th receiver in a cyclic manner, e.g., the first transmitter causes interference only to the Kth receiver. The impact of noiseless feedback on the capacity of this channel is studied by focusing on the Gaussian cyclic Z-interference channel. To this end, the symmetric feedback capacity of the linear shift deterministic cyclic Z-interference channel (LD-CZIC) is completely characterized for all interference regimes. Using insights from the linear deterministic channel model, the symmetric feedback capacity of the Gaussian cyclic Z-interference channel is characterized up to within a constant number of bits. As a byproduct of the constant gap result, the symmetric generalized degrees of freedom with feedback for the Gaussian cyclic Z-interference channel are also characterized. These results highlight that the symmetric feedback capacities for both linear and Gaussian channel models are in general functions of K, the number of users. Furthermore, the capacity gain obtained due to feedback decreases as K increases.

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arXiv2012

On Convergence Rate of Scalar Hegselmann-Krause Dynamics

In this work, we derive a new upper bound on the termination time of the Hegselmann-Krause model for opinion dynamics. Using a novel method, we show that the termination rate of this dynamics happens no longer than $O(n^3)$ which improves the best known upper bound of $O(n^4)$ by a factor of $n$ .

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arXiv2012

Degrees of Freedom Region of the MIMO Interference Channel with Output Feedback and Delayed CSIT

The two-user multiple-input multiple-output (MIMO) interference channel (IC) with arbitrary number of antennas at each terminal is considered and the degrees of freedom (DoF) region is characterized in the presence of noiseless channel output feedback from each receiver to its respective transmitter and availability of delayed channel state information at the transmitters (CSIT). It is shown that having output feedback and delayed CSIT can strictly enlarge the DoF region of the MIMO IC when compared to the case in which only delayed CSIT is present. The proposed coding schemes that achieve the corresponding DoF region with feedback and delayed CSIT utilize both resources, i.e., feedback and delayed CSIT in a non-trivial manner. It is also shown that the DoF region with local feedback and delayed CSIT is equal to the DoF region with global feedback and delayed CSIT, i.e., local feedback and delayed CSIT is equivalent to global feedback and delayed CSIT from the perspective of the degrees of freedom region. The converse is proved for a stronger setting in which the channels to the two receivers need not be statistically equivalent.

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arXiv2012

Tight Bounds on the Redundancy of Huffman Codes

In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of such Huffman codes, which yields in a tight upper bound. We also derive a tight lower bound for the redundancy under the same assumption. We further apply the method introduced in this paper to other related problems. It is shown that several other previously known bounds with different constraints follow immediately from our results.

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arXiv2012

On X-Channels with Feedback and Delayed CSI

The sum degrees of freedom (DoF) of the two-user MIMO X-channel is characterized in the presence of output feedback and delayed channel state information (CSI). The number of antennas at each transmitters is assumed to be M and the number of antennas at each of the receivers is assumed to be N. It is shown that the sum DoF of the two-user MIMO X-channel is the same as the sum DoF of a two-user MIMO broadcast channel with 2M transmit antennas, and N antennas at each receiver. Hence, for this symmetric antenna configuration, there is no performance loss in the sum degrees of freedom due to the distributed nature of the transmitters. This result highlights the usefulness of feedback and delayed CSI for the MIMO X-channel. The K-user X-channel with single antenna at each transmitter and each receiver is also studied. In this network, each transmitter has a message intended for each receiver. For this network, it is shown that the sum DoF with partial output feedback alone is at least 2K/(K+1). This lower bound is strictly better than the best lower bound known for the case of delayed CSI assumption for all values of K.

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arXiv2011

Smart Meter Privacy: A Utility-Privacy Framework

End-user privacy in smart meter measurements is a well-known challenge in the smart grid. The solutions offered thus far have been tied to specific technologies such as batteries or assumptions on data usage. Existing solutions have also not quantified the loss of benefit (utility) that results from any such privacy-preserving approach. Using tools from information theory, a new framework is presented that abstracts both the privacy and the utility requirements of smart meter data. This leads to a novel privacy-utility tradeoff problem with minimal assumptions that is tractable. Specifically for a stationary Gaussian Markov model of the electricity load, it is shown that the optimal utility-and-privacy preserving solution requires filtering out frequency components that are low in power, and this approach appears to encompass most of the proposed privacy approaches.

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arXiv2011

Graph-Constrained Group Testing

Non-adaptive group testing involves grouping arbitrary subsets of $n$ items into different pools. Each pool is then tested and defective items are identified. A fundamental question involves minimizing the number of pools required to identify at most $d$ defective items. Motivated by applications in network tomography, sensor networks and infection propagation, a variation of group testing problems on graphs is formulated. Unlike conventional group testing problems, each group here must conform to the constraints imposed by a graph. For instance, items can be associated with vertices and each pool is any set of nodes that must be path connected. In this paper, a test is associated with a random walk. In this context, conventional group testing corresponds to the special case of a complete graph on $n$ vertices. For interesting classes of graphs a rather surprising result is obtained, namely, that the number of tests required to identify $d$ defective items is substantially similar to what is required in conventional group testing problems, where no such constraints on pooling is imposed. Specifically, if T(n) corresponds to the mixing time of the graph $G$, it is shown that with $m=O(d^2T^2(n)\log(n/d))$ non-adaptive tests, one can identify the defective items. Consequently, for the Erdos-Renyi random graph $G(n,p)$, as well as expander graphs with constant spectral gap, it follows that $m=O(d^2\log^3n)$ non-adaptive tests are sufficient to identify $d$ defective items. Next, a specific scenario is considered that arises in network tomography, for which it is shown that $m=O(d^3\log^3n)$ non-adaptive tests are sufficient to identify $d$ defective items. Noisy counterparts of the graph constrained group testing problem are considered, for which parallel results are developed. We also briefly discuss extensions to compressive sensing on graphs.

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arXiv2010

On the Capacity of Non-Coherent Network Coding

We consider the problem of multicasting information from a source to a set of receivers over a network where intermediate network nodes perform randomized network coding operations on the source packets. We propose a channel model for the non-coherent network coding introduced by Koetter and Kschischang in [6], that captures the essence of such a network operation, and calculate the capacity as a function of network parameters. We prove that use of subspace coding is optimal, and show that, in some cases, the capacity-achieving distribution uses subspaces of several dimensions, where the employed dimensions depend on the packet length. This model and the results also allow us to give guidelines on when subspace coding is beneficial for the proposed model and by how much, in comparison to a coding vector approach, from a capacity viewpoint. We extend our results to the case of multiple source multicast that creates a virtual multiple access channel.

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arXiv2010

Approximate Capacity of Gaussian Interference-Relay Networks with Weak Cross Links

In this paper we study a Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We focus on a two-stage relay-interference network where there are weak cross-links, causing the networks to behave like a chain of Z Gaussian channels. For these Gaussian ZZ and ZS networks, we establish an approximate characterization of the rate region. The outer bounds to the capacity region are established using genie-aided techniques that yield bounds sharper than the traditional cut-set outer bounds. For the inner bound of the ZZ network, we propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This technique allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. For both the ZZ and ZS networks, we establish a new network decomposition technique that (approximately) achieves the capacity region. We use insights gained from an exact characterization of the corresponding linear deterministic version of the problems, in order to establish the approximate characterization for Gaussian networks.

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arXiv2009

An Estimation Theoretic Approach for Sparsity Pattern Recovery in the Noisy Setting

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on the scaling law of the number of measurements for successful support recovery have been derived where the main focus is on random Gaussian measurement matrices. In this paper, we investigate the noisy support recovery problem from an estimation theoretic point of view, where no specific assumption is made on the underlying measurement matrix. The linear measurements are perturbed by additive white Gaussian noise. We define the output of a support estimator to be a set of position values in increasing order. We set the error between the true and estimated supports as the $\ell_2$-norm of their difference. On the one hand, this choice allows us to use the machinery behind the $\ell_2$-norm error metric and on the other hand, converts the support recovery into a more intuitive and geometrical problem. First, by using the Hammersley-Chapman-Robbins (HCR) bound, we derive a fundamental lower bound on the performance of any \emph{unbiased} estimator of the support set. This lower bound provides us with necessary conditions on the number of measurements for reliable $\ell_2$-norm support recovery, which we specifically evaluate for uniform Gaussian measurement matrices. Then, we analyze the maximum likelihood estimator and derive conditions under which the HCR bound is achievable. This leads us to the number of measurements for the optimum decoder which is sufficient for reliable $\ell_2$-norm support recovery. Using this framework, we specifically evaluate sufficient conditions for uniform Gaussian measurement matrices.

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