arXiv subjects

Alexandros G. Dimakis

Publications and source records attributed to Alexandros G. Dimakis.

At least 127 records · Page 7Linked to original sources

arXiv2013

Base-Station Assisted Device-to-Device Communications for High-Throughput Wireless Video Networks

We propose a new scheme for increasing the throughput of video files in cellular communications systems. This scheme exploits (i) the redundancy of user requests as well as (ii) the considerable storage capacity of smartphones and tablets. Users cache popular video files and - after receiving requests from other users - serve these requests via device-to-device localized transmissions. The file placement is optimal when a central control knows a priori the locations of wireless devices when file requests occur. However, even a purely random caching scheme shows only a minor performance loss compared to such a genie-aided scheme. We then analyze the optimal collaboration distance, trading off frequency reuse with the probability of finding a requested file within the collaboration distance. We show that an improvement of spectral efficiency of one to two orders of magnitude is possible, even if there is not very high redundancy in video requests.

cs.NI↗

arXiv2013

Local Graph Coloring and Index Coding

We present a novel upper bound for the optimal index coding rate. Our bound uses a graph theoretic quantity called the local chromatic number. We show how a good local coloring can be used to create a good index code. The local coloring is used as an alignment guide to assign index coding vectors from a general position MDS code. We further show that a natural LP relaxation yields an even stronger index code. Our bounds provably outperform the state of the art on index coding but at most by a constant factor.

cs.IT↗

arXiv2013

XORing Elephants: Novel Erasure Codes for Big Data

Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard design choice and their high repair cost is often considered an unavoidable price to pay for high storage efficiency and high reliability. This paper shows how to overcome this limitation. We present a novel family of erasure codes that are efficiently repairable and offer higher reliability compared to Reed-Solomon codes. We show analytically that our codes are optimal on a recently identified tradeoff between locality and minimum distance. We implement our new codes in Hadoop HDFS and compare to a currently deployed HDFS module that uses Reed-Solomon codes. Our modified HDFS implementation shows a reduction of approximately 2x on the repair disk I/O and repair network traffic. The disadvantage of the new coding scheme is that it requires 14% more storage compared to Reed-Solomon codes, an overhead shown to be information theoretically optimal to obtain locality. Because the new codes repair failures faster, this provides higher reliability, which is orders of magnitude higher compared to replication.

cs.IT↗

arXiv2012

On the Delay Advantage of Coding in Packet Erasure Networks

We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sub-linear term in the block delay required for unicasting $n$ packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding scales at least as $\sqrt{n}$. Our analysis of the delay function for the routing strategy involves a major technical challenge of computing the expectation of the maximum of two negative binomial random variables. This problem has been studied previously and we derive the first exact characterization which may be of independent interest. We also use a martingale bounded differences argument to show that the actual coding delay is tightly concentrated around its expectation.

cs.IT↗

arXiv2012

Connectivity and equilibrium in random games

We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implications for many deterministic graphs and generalize known results for random games on the complete graph. In particular, our results imply that the probability that bounded degree graphs have pure Nash equilibria is exponentially small in the size of the graph and yield a simple algorithm that finds small nonexistence certificates for a large family of graphs. Then we show that in any strongly connected graph of n vertices with expansion $(1+Ω(1))\log_2(n)$ the distribution of the number of equilibria approaches the Poisson distribution with parameter 1, asymptotically as $n \to +\infty$.

math.PR↗

arXiv2012

Scaling Behaviors of Wireless Device-to-Device Communications with Distributed Caching

We analyze a novel architecture for caching popular video content to enable wireless device-to-device collaboration. We focus on the asymptotic scaling characteristics and show how they depends on video content popularity statistics. We identify a fundamental conflict between collaboration distance and interference and show how to optimize the transmission power to maximize frequency reuse. Our main result is a closed form expression of the optimal collaboration distance as a function of the model parameters. Under the common assumption of a Zipf distribution for content reuse, we show that if the Zipf exponent is greater than 1, it is possible to have a number of D2D interference-free collaboration pairs that scales linearly in the number of nodes. If the Zipf exponent is smaller than 1, we identify the best possible scaling in the number of D2D collaborating links. Surprisingly, a very simple distributed caching policy achieves the optimal scaling behavior and therefore there is no need to centrally coordinate what each node is caching.

cs.NI↗

arXiv2012

Distributed Storage Allocations

We examine the problem of allocating a given total storage budget in a distributed storage system for maximum reliability. A source has a single data object that is to be coded and stored over a set of storage nodes; it is allowed to store any amount of coded data in each node, as long as the total amount of storage used does not exceed the given budget. A data collector subsequently attempts to recover the original data object by accessing only the data stored in a random subset of the nodes. By using an appropriate code, successful recovery can be achieved whenever the total amount of data accessed is at least the size of the original data object. The goal is to find an optimal storage allocation that maximizes the probability of successful recovery. This optimization problem is challenging in general because of its combinatorial nature, despite its simple formulation. We study several variations of the problem, assuming different allocation models and access models. The optimal allocation and the optimal symmetric allocation (in which all nonempty nodes store the same amount of data) are determined for a variety of cases. Our results indicate that the optimal allocations often have nonintuitive structure and are difficult to specify. We also show that depending on the circumstances, coding may or may not be beneficial for reliable storage.

cs.IT↗

arXiv2012

Wireless Device-to-Device Communications with Distributed Caching

We introduce a novel wireless device-to-device (D2D) collaboration architecture that exploits distributed storage of popular content to enable frequency reuse. We identify a fundamental conflict between collaboration distance and interference and show how to optimize the transmission power to maximize frequency reuse. Our analysis depends on the user content request statistics which are modeled by a Zipf distribution. Our main result is a closed form expression of the optimal collaboration distance as a function of the content reuse distribution parameters. We show that if the Zipf exponent of the content reuse distribution is greater than 1, it is possible to have a number of D2D interference-free collaboration pairs that scales linearly in the number of nodes. If the Zipf exponent is smaller than 1, we identify the best possible scaling in the number of D2D collaborating links. Surprisingly, a very simple distributed caching policy achieves the optimal scaling behavior and therefore there is no need to centrally coordinate what each node is caching.

cs.IT↗

arXiv2012

Femtocaching and Device-to-Device Collaboration: A New Architecture for Wireless Video Distribution

We present a new architecture to handle the ongoing explosive increase in the demand for video content in wireless networks. It is based on distributed caching of the content in femto-basestations with small or non-existing backhaul capacity but with considerable storage space, called helper nodes. We also consider using the mobile terminals themselves as caching helpers, which can distribute video through device-to-device communications. This approach allows an improvement in the video throughput without deployment of any additional infrastructure. The new architecture can improve video throughput by one to two orders-of-magnitude.

cs.NI↗

arXiv2012

Allocations for Heterogenous Distributed Storage

We study the problem of storing a data object in a set of data nodes that fail independently with given probabilities. Our problem is a natural generalization of a homogenous storage allocation problem where all the nodes had the same reliability and is naturally motivated for peer-to-peer and cloud storage systems with different types of nodes. Assuming optimal erasure coding (MDS), the goal is to find a storage allocation (i.e, how much to store in each node) to maximize the probability of successful recovery. This problem turns out to be a challenging combinatorial optimization problem. In this work we introduce an approximation framework based on large deviation inequalities and convex optimization. We propose two approximation algorithms and study the asymptotic performance of the resulting allocations.

cs.IT↗

arXiv2011

LDPC Codes for Compressed Sensing

We present a mathematical connection between channel coding and compressed sensing. In particular, we link, on the one hand, \emph{channel coding linear programming decoding (CC-LPD)}, which is a well-known relaxation o maximum-likelihood channel decoding for binary linear codes, and, on the other hand, \emph{compressed sensing linear programming decoding (CS-LPD)}, also known as basis pursuit, which is a widely used linear programming relaxation for the problem of finding the sparsest solution of an under-determined system of linear equations. More specifically, we establis a tight connection between CS-LPD based on a zero-one measurement matrix over the reals and CC-LPD of the binary linear channel code that is obtained by viewing this measurement matrix as a binary parity-check matrix. This connection allows the translation of performance guarantees from one setup to the other. The main message of this paper is that parity-check matrices of "good" channel codes can be used as provably "good" measurement matrices under basis pursuit. In particular, we provide the first deterministic construction of compressed sensing measurement matrices with an order-optimal number of rows using high-girth low-density parity-check (LDPC) codes constructed by Gallager.

cs.IT↗

arXiv2011

Simple Regenerating Codes: Network Coding for Cloud Storage

Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem: if a node storing encoded information fails, in order to maintain the same level of reliability we need to create encoded information at a new node. One of the main open problems in this emerging area has been the design of simple coding schemes that allow exact and low cost repair of failed nodes and have high data rates. In particular, all prior known explicit constructions have data rates bounded by 1/2. In this paper we introduce the first family of distributed storage codes that have simple look-up repair and can achieve arbitrarily high rates. Our constructions are very simple to implement and perform exact repair by simple XORing of packets. We experimentally evaluate the proposed codes in a realistic cloud storage simulator and show significant benefits in both performance and reliability compared to replication and standard Reed-Solomon codes.

cs.IT↗

arXiv2011

The Impact of Mobility on Gossip Algorithms

The influence of node mobility on the convergence time of averaging gossip algorithms in networks is studied. It is shown that a small number of fully mobile nodes can yield a significant decrease in convergence time. A method is developed for deriving lower bounds on the convergence time by merging nodes according to their mobility pattern. This method is used to show that if the agents have one-dimensional mobility in the same direction the convergence time is improved by at most a constant. Upper bounds are obtained on the convergence time using techniques from the theory of Markov chains and show that simple models of mobility can dramatically accelerate gossip as long as the mobility paths significantly overlap. Simulations verify that different mobility patterns can have significantly different effects on the convergence of distributed algorithms.

cs.NI↗

arXiv2011

Distributed Storage Allocations for Optimal Delay

We examine the problem of creating an encoded distributed storage representation of a data object for a network of mobile storage nodes so as to achieve the optimal recovery delay. A source node creates a single data object and disseminates an encoded representation of it to other nodes for storage, subject to a given total storage budget. A data collector node subsequently attempts to recover the original data object by contacting other nodes and accessing the data stored in them. By using an appropriate code, successful recovery is achieved when the total amount of data accessed is at least the size of the original data object. The goal is to find an allocation of the given budget over the nodes that optimizes the recovery delay incurred by the data collector; two objectives are considered: (i) maximization of the probability of successful recovery by a given deadline, and (ii) minimization of the expected recovery delay. We solve the problem completely for the second objective in the case of symmetric allocations (in which all nonempty nodes store the same amount of data), and show that the optimal symmetric allocation for the two objectives can be quite different. A simple data dissemination and storage protocol for a mobile delay-tolerant network is evaluated under various scenarios via simulations. Our results show that the choice of storage allocation can have a significant impact on the recovery delay performance, and that coding may or may not be beneficial depending on the circumstances.

cs.IT↗

arXiv2011

Repair Optimal Erasure Codes through Hadamard Designs

In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it communication} required to exactly rebuild a storage node after a failure arises. This repair bandwidth depends on the structure of the storage code and the repair strategies used to restore the lost data. Designing high-rate maximum-distance separable (MDS) codes that achieve the optimum repair communication has been a well-known open problem. In this work, we use Hadamard matrices to construct the first explicit 2-parity MDS storage code with optimal repair properties for all single node failures, including the parities. Our construction relies on a novel method of achieving perfect interference alignment over finite fields with a finite file size, or number of extensions. We generalize this construction to design $m$-parity MDS codes that achieve the optimum repair communication for single systematic node failures and show that there is an interesting connection between our $m$-parity codes and the systematic-repair optimal permutation-matrix based codes of Tamo {\it et al.} \cite{Tamo} and Cadambe {\it et al.} \cite{PermCodes_ISIT, PermCodes}.

cs.IT↗

arXiv2011

Distributed Storage Codes through Hadamard Designs

In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the storage code and the repair strategies used to restore the lost data. Minimizing it requires that undesired data during a repair align in the smallest possible spaces, using the concept of interference alignment (IA). Here, a points-on-a-lattice representation of the symbol extension IA of Cadambe {\it et al.} provides cues to perfect IA instances which we combine with fundamental properties of Hadamard matrices to construct a new storage code with favorable repair properties. Specifically, we build an explicit $(k+2,k)$ storage code over $\mathbb{GF}(3)$, whose single systematic node failures can be repaired with bandwidth that matches exactly the theoretical minimum. Moreover, the repair of single parity node failures generates at most the same repair bandwidth as any systematic node failure. Our code can tolerate any single node failure and any pair of failures that involves at most one systematic failure.

cs.IT↗

arXiv2011

Interference Alignment as a Rank Constrained Rank Minimization

We show that the maximization of the sum degrees-of-freedom for the static flat-fading multiple-input multiple-output (MIMO) interference channel is equivalent to a rank constrained rank minimization problem (RCRM), when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) so that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and low-rank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the normalized sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be tuned for the multi-cell interference channel. Furthermore, we experimentally show that in many cases the proposed algorithm attains perfect interference alignment and in some cases outperforms previous approaches for finding precoding and zero-forcing matrices for interference alignment.

cs.IT↗

arXiv2011

Reweighted LP Decoding for LDPC Codes

We introduce a novel algorithm for decoding binary linear codes by linear programming. We build on the LP decoding algorithm of Feldman et al. and introduce a post-processing step that solves a second linear program that reweights the objective function based on the outcome of the original LP decoder output. Our analysis shows that for some LDPC ensembles we can improve the provable threshold guarantees compared to standard LP decoding. We also show significant empirical performance gains for the reweighted LP decoding algorithm with very small additional computational complexity.

cs.IT↗