arXiv subjects

Ahmad Beirami

Publications and source records attributed to Ahmad Beirami.

90 records · Page 5Linked to original sources

arXiv2014

Universal Compression of a Mixture of Parametric Sources with Side Information

This paper investigates the benefits of the side information on the universal compression of sequences from a mixture of $K$ parametric sources. The output sequence of the mixture source is chosen from the source $i \in \{1,\ldots ,K\}$ with a $d_i$-dimensional parameter vector at random according to probability vector $\mathbf{w} = (w_1,\ldots,w_K)$. The average minimax redundancy of the universal compression of a new random sequence of length $n$ is derived when the encoder and the decoder have a common side information of $T$ sequences generated independently by the mixture source. Necessary and sufficient conditions on the distribution $\mathbf{w}$ and the mixture parameter dimensions $\mathbf{d} = (d_1,\ldots,d_K)$ are determined such that the side information provided by the previous sequences results in a reduction in the first-order term of the average codeword length compared with the universal compression without side information. Further, it is proved that the optimal compression with side information corresponds to the clustering of the side information sequences from the mixture source. Then, a clustering technique is presented to better utilize the side information by classifying the data sequences from a mixture source. Finally, the performance of the clustering on the universal compression with side information is validated using computer simulations on real network data traces.

cs.IT↗

arXiv2014

Packet-Level Network Compression: Realization and Scaling of the Network-Wide Benefits

The existence of considerable amount of redundancy in the Internet traffic at the packet level has stimulated the deployment of packet-level redundancy elimination techniques within the network by enabling network nodes to memorize data packets. Redundancy elimination results in traffic reduction which in turn improves the efficiency of network links. In this paper, the concept of network compression is introduced that aspires to exploit the statistical correlation beyond removing large duplicate strings from the flow to better suppress redundancy. In the first part of the paper, we introduce "memory-assisted compression", which utilizes the memorized content within the network to learn the statistics of the information source generating the packets which can then be used toward reducing the length of codewords describing the packets emitted by the source. Using simulations on data gathered from real network traces, we show that memory-assisted compression can result in significant traffic reduction. In the second part of the paper, we study the scaling of the average network-wide benefits of memory-assisted compression. We discuss routing and memory placement problems in network for the reduction of overall traffic. We derive a closed-form expression for the scaling of the gain in Erdos-Renyi random network graphs, where obtain a threshold value for the number of memories deployed in a random graph beyond which network-wide benefits start to shine. Finally, the network-wide benefits are studied on Internet-like scale-free networks. We show that non-vanishing network compression gain is obtained even when only a tiny fraction of the total number of nodes in the network are memory-enabled.

cs.NI↗

arXiv2013

A Framework for Investigating the Performance of Chaotic-Map Truly Random Number Generators

In this paper, we approximate the hidden Markov model of chaotic-map truly random number generators (TRNGs) and describe its fundamental limits based on the approximate entropy-rate of the underlying bit-generation process. We demonstrate that entropy-rate plays a key role in the performance and robustness of chaotic-map TRNGs, which must be taken into account in the circuit design optimization. We further derive optimality conditions for post-processing units that extract truly random bits from a raw-RNG.

cs.IT↗

arXiv2013

Theoretical Analysis of the Characteristic Impedance in Metal-Insulator-Metal Plasmonic Transmission Lines

We propose a closed form formulation for the impedance of the Metal-Insulator-Metal (MIM) plasmonic transmission lines by solving the Maxwell's equations. We provide approximations for thin and thick insulator layers sandwiched between metallic layers. In the case of very thin dielectric layer, the surface waves on both interfaces are strongly coupled resulting in an almost linear dependence of the impedance of the plasmonic transmission line on the thickness of the insulator layer. On the other hand, for very thick insulator layer, the impedance does not vary with the insulator layer thickness due to the weak-coupling/decoupling of the surface waves on each metal-insulator interface. We demonstrate the effectiveness of our proposed formulation using two test scenarios, namely, almost zero reflection in Tee-junction and reflection from line discontinuity in the design of Bragg reflectors, where we compare our formulation against previously published results.

physics.optics↗

arXiv2012

Network Compression: Memory-Assisted Universal Coding of Sources with Correlated Parameters

In this paper, we propose {\em distributed network compression via memory}. We consider two spatially separated sources with correlated unknown source parameters. We wish to study the universal compression of a sequence of length $n$ from one of the sources provided that the decoder has access to (i.e., memorized) a sequence of length $m$ from the other source. In this setup, the correlation does not arise from symbol-by-symbol dependency of two outputs from the two sources (as in Slepian-Wolf setup). Instead, the two sequences are correlated because they are originated from the two sources with \emph{unknown} correlated parameters. The finite-length nature of the compression problem at hand requires considering a notion of almost lossless source coding, where coding incurs an error probability $p_e(n)$ that vanishes as sequence length $n$ grows to infinity. We obtain bounds on the redundancy of almost lossless codes when the decoder has access to a random memory of length $m$ as a function of the sequence length $n$ and the permissible error probability $p_e(n)$. Our results demonstrate that distributed network compression via memory has the potential to significantly improve over conventional end-to-end compression when sufficiently large memory from previous communications is available to the decoder.

cs.IT↗

arXiv2012

On Lossless Universal Compression of Distributed Identical Sources

Slepian-Wolf theorem is a well-known framework that targets almost lossless compression of (two) data streams with symbol-by-symbol correlation between the outputs of (two) distributed sources. However, this paper considers a different scenario which does not fit in the Slepian-Wolf framework. We consider two identical but spatially separated sources. We wish to study the universal compression of a sequence of length $n$ from one of the sources provided that the decoder has access to (i.e., memorized) a sequence of length $m$ from the other source. Such a scenario occurs, for example, in the universal compression of data from multiple mirrors of the same server. In this setup, the correlation does not arise from symbol-by-symbol dependency of two outputs from the two sources. Instead, the sequences are correlated through the information that they contain about the unknown source parameter. We show that the finite-length nature of the compression problem at hand requires considering a notion of almost lossless source coding, where coding incurs an error probability $p_e(n)$ that vanishes with sequence length $n$. We obtain a lower bound on the average minimax redundancy of almost lossless codes as a function of the sequence length $n$ and the permissible error probability $p_e$ when the decoder has a memory of length $m$ and the encoders do not communicate. Our results demonstrate that a strict performance loss is incurred when the two encoders do not communicate even when the decoder knows the unknown parameter vector (i.e., $m \to \infty$).

cs.IT↗

arXiv2012

Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map

In this paper, we introduce a novel discrete chaotic map named zigzag map that demonstrates excellent chaotic behaviors and can be utilized in Truly Random Number Generators (TRNGs). We comprehensively investigate the map and explore its critical chaotic characteristics and parameters. We further present two circuit implementations for the zigzag map based on the switched current technique as well as the current-mode affine interpolation of the breakpoints. In practice, implementation variations can deteriorate the quality of the output sequence as a result of variation of the chaotic map parameters. In order to quantify the impact of variations on the map performance, we model the variations using a combination of theoretical analysis and Monte-Carlo simulations on the circuits. We demonstrate that even in the presence of the map variations, a TRNG based on the zigzag map passes all of the NIST 800-22 statistical randomness tests using simple post processing of the output data.

math.DS↗

arXiv2012

A Realizable Modified Tent Map for True Random Number Generation

Tent map is a discrete-time piecewise-affine I/O characteristic curve, which is used for chaos-based applications, such as true random number generation. However, tent map suffers from the inability to maintain the output state confined to the input range under noise and process variations. In this paper, we propose a modified tent map, which is interchangeable with the tent map for practical applications. In the proposed modified tent map, the confinement problem is solved while maintaining the functionality of the tent map. We also demonstrate simulation results for the circuit implementation of the presented modified tent map for true random number generation.

math.DS↗

arXiv2012

Data Gathering in Networks of Bacteria Colonies: Collective Sensing and Relaying Using Molecular Communication

The prospect of new biological and industrial applications that require communication in micro-scale, encourages research on the design of bio-compatible communication networks using networking primitives already available in nature. One of the most promising candidates for constructing such networks is to adapt and engineer specific types of bacteria that are capable of sensing, actuation, and above all, communication with each other. In this paper, we describe a new architecture for networks of bacteria to form a data collecting network, as in traditional sensor networks. The key to this architecture is the fact that the node in the network itself is a bacterial colony; as an individual bacterium (biological agent) is a tiny unreliable element with limited capabilities. We describe such a network under two different scenarios. We study the data gathering (sensing and multihop communication) scenario as in sensor networks followed by the consensus problem in a multi-node network. We will explain as to how the bacteria in the colony collectively orchestrate their actions as a node to perform sensing and relaying tasks that would not be possible (at least reliably) by an individual bacterium. Each single bacterium in the colony forms a belief by sensing external parameter (e.g., a molecular signal from another node) from the medium and shares its belief with other bacteria in the colony. Then, after some interactions, all the bacteria in the colony form a common belief and act as a single node. We will model the reception process of each individual bacteria and will study its impact on the overall functionality of a node. We will present results on the reliability of the multihop communication for data gathering scenario as well as the speed of convergence in the consensus scenario.

cs.IT↗

arXiv2012

Results on the Fundamental Gain of Memory-Assisted Universal Source Coding

Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would not perform well over the finite-length sequences. Recently, we proposed a framework called memory-assisted universal compression that holds a significant promise for reducing the amount of redundant data from the finite-length sequences. The proposed compression scheme is based on the observation that it is possible to learn source statistics (by memorizing previous sequences from the source) at some intermediate entities and then leverage the memorized context to reduce redundancy of the universal compression of finite-length sequences. We first present the fundamental gain of the proposed memory-assisted universal source coding over conventional universal compression (without memorization) for a single parametric source. Then, we extend and investigate the benefits of the memory-assisted universal source coding when the data sequences are generated by a compound source which is a mixture of parametric sources. We further develop a clustering technique within the memory-assisted compression framework to better utilize the memory by classifying the observed data sequences from a mixture of parametric sources. Finally, we demonstrate through computer simulations that the proposed joint memorization and clustering technique can achieve up to 6-fold improvement over the traditional universal compression technique when a mixture of non-binary Markov sources is considered.

cs.IT↗

arXiv2012

Memory-Assisted Universal Compression of Network Flows

Recently, the existence of considerable amount of redundancy in the Internet traffic has stimulated the deployment of several redundancy elimination techniques within the network. These techniques are often based on either packet-level Redundancy Elimination (RE) or Content-Centric Networking (CCN). However, these techniques cannot exploit sub-packet redundancies. Further, other alternative techniques such as the end-to-end universal compression solutions would not perform well either over the Internet traffic, as such techniques require infinite length traffic to effectively remove redundancy. This paper proposes a memory-assisted universal compression technique that holds a significant promise for reducing the amount of traffic in the networks. The proposed work is based on the observation that if a source is to be compressed and sent over a network, the associated universal code entails a substantial overhead in transmission due to finite length traffic. However, intermediate nodes can learn the source statistics and this can be used to reduce the cost of describing the source statistics, reducing the transmission overhead for such traffics. We present two algorithms (statistical and dictionary-based) for the memory-assisted universal lossless compression of information sources. These schemes are universal in the sense that they do not require any prior knowledge of the traffic's statistical distribution. We demonstrate the effectiveness of both algorithms and characterize the memorization gain using the real Internet traces. Furthermore, we apply these compression schemes to Internet-like power-law graphs and solve the routing problem for compressed flows.

cs.IT↗

arXiv2012

Memory-Assisted Universal Source Coding

The problem of the universal compression of a sequence from a library of several small to moderate length sequences from similar context arises in many practical scenarios, such as the compression of the storage data and the Internet traffic. In such scenarios, it is often required to compress and decompress every sequence individually. However, the universal compression of the individual sequences suffers from significant redundancy overhead. In this paper, we aim at answering whether or not having a memory unit in the middle can result in a fundamental gain in the universal compression. We present the problem setup in the most basic scenario consisting of a server node $S$, a relay node $R$ (i.e., the memory unit), and a client node $C$. We assume that server $S$ wishes to send the sequence $x^n$ to the client $C$ who has never had any prior communication with the server, and hence, is not capable of memorization of the source context. However, $R$ has previously communicated with $S$ to forward previous sequences from $S$ to the clients other than $C$, and thus, $R$ has memorized a context $y^m$ shared with $S$. Note that if the relay node was absent the source could possibly apply universal compression to $x^n$ and transmit to $C$ whereas the presence of memorized context at $R$ can possibly reduce the communication overhead in $S$-$R$ link. In this paper, we investigate the fundamental gain of the context memorization in the memory-assisted universal compression of the sequence $x^n$ over conventional universal source coding by providing a lower bound on the gain of memory-assisted source coding.

cs.IT↗

arXiv2012

A Performance Metric for Discrete-Time Chaos-Based Truly Random Number Generators

In this paper, we develop an information entropy based metric that represents the statistical quality of the generated binary sequence in Truly Random Number Generators (TRNG). The metric can be used for the design and optimization of the TRNG circuits as well as the development of efficient post-processing units for recovering the degraded statistical characteristics of the signal due to process variations.

cs.IT↗

arXiv2011

Exact Modeling of the Performance of Random Linear Network Coding in Finite-buffer Networks

In this paper, we present an exact model for the analysis of the performance of Random Linear Network Coding (RLNC) in wired erasure networks with finite buffers. In such networks, packets are delayed due to either random link erasures or blocking by full buffers. We assert that because of RLNC, the content of buffers have dependencies which cannot be captured directly using the classical queueing theoretical models. We model the performance of the network using Markov chains by a careful derivation of the buffer occupancy states and their transition rules. We verify by simulations that the proposed framework results in an accurate measure of the network throughput offered by RLNC. Further, we introduce a class of acyclic networks for which the number of state variables is significantly reduced.

cs.IT↗

arXiv2011

Results on the Redundancy of Universal Compression for Finite-Length Sequences

In this paper, we investigate the redundancy of universal coding schemes on smooth parametric sources in the finite-length regime. We derive an upper bound on the probability of the event that a sequence of length $n$, chosen using Jeffreys' prior from the family of parametric sources with $d$ unknown parameters, is compressed with a redundancy smaller than $(1-ε)\frac{d}{2}\log n$ for any $ε>0$. Our results also confirm that for large enough $n$ and $d$, the average minimax redundancy provides a good estimate for the redundancy of most sources. Our result may be used to evaluate the performance of universal source coding schemes on finite-length sequences. Additionally, we precisely characterize the minimax redundancy for two--stage codes. We demonstrate that the two--stage assumption incurs a negligible redundancy especially when the number of source parameters is large. Finally, we show that the redundancy is significant in the compression of small sequences.

cs.IT↗

arXiv2011

On the Network-Wide Gain of Memory-Assisted Source Coding

Several studies have identified a significant amount of redundancy in the network traffic. For example, it is demonstrated that there is a great amount of redundancy within the content of a server over time. This redundancy can be leveraged to reduce the network flow by the deployment of memory units in the network. The question that arises is whether or not the deployment of memory can result in a fundamental improvement in the performance of the network. In this paper, we answer this question affirmatively by first establishing the fundamental gains of memory-assisted source compression and then applying the technique to a network. Specifically, we investigate the gain of memory-assisted compression in random network graphs consisted of a single source and several randomly selected memory units. We find a threshold value for the number of memories deployed in a random graph and show that if the number of memories exceeds the threshold we observe network-wide reduction in the traffic.

cs.IT↗

arXiv2011

Capacity of Discrete Molecular Diffusion Channels

In diffusion-based molecular communications, messages can be conveyed via the variation in the concentration of molecules in the medium. In this paper, we intend to analyze the achievable capacity in transmission of information from one node to another in a diffusion channel. We observe that because of the molecular diffusion in the medium, the channel possesses memory. We then model the memory of the channel by a two-step Markov chain and obtain the equations describing the capacity of the diffusion channel. By performing a numerical analysis, we obtain the maximum achievable rate for different levels of the transmitter power, i.e., the molecule production rate.

cs.IT↗

arXiv2011

Consensus Problem under Diffusion-based Molecular Communication

We investigate the consensus problem in a network where nodes communicate via diffusion-based molecular communication (DbMC). In DbMC, messages are conveyed via the variation in the concentration of molecules in the medium. Every node acquires sensory information about the environment. Communication enables the nodes to reach the best estimate for that measurement, e.g., the average of the initial estimates by all nodes. We consider an iterative method for communication among nodes that enables information spreading and averaging in the network. We show that the consensus can be attained after a finite number of iterations and variance of estimates of nodes can be made arbitrarily small via communication.

cs.IT↗