Elza Erkip

Polytechnic Institute of New York University, Brooklyn, New York, United States

Are you Elza Erkip?

Claim your profile

Publications (228)183.68 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be recovered from their under-determined set of linear projections. Currently, there is a large gap between the complexity of the structures studied in the area of compressed sensing and those employed by the state-of-the-art compression codes. Recent results in the literature on deterministic signals aim at bridging this gap through devising compressed sensing decoders that employ compression codes. This paper focuses on structured stochastic processes and studies the application of rate-distortion codes to compressed sensing of such signals. The performance of the formerly-proposed compressible signal pursuit (CSP) algorithm is studied in this stochastic setting. It is proved that in the very low distortion regime, as the blocklength grows to infinity, the CSP algorithm reliably and robustly recovers $n$ instances of a stationary process from random linear projections as long as their count is slightly more than $n$ times the rate-distortion dimension (RDD) of the source. It is also shown that under some regularity conditions, the RDD of a stationary process is equal to its information dimension (ID). This connection establishes the optimality of the CSP algorithm at least for memoryless stationary sources, for which the fundamental limits are known. Finally, it is shown that the CSP algorithm combined by a family of universal variable-length fixed-distortion compression codes yields a family of universal compressed sensing recovery algorithms.
    No preview · Article · Jan 2016
  • Source
    Yuanpeng Liu · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: In a two-user channel, completion time refers to the number of channel uses spent by each user to transmit a bit pool with some given size. In this paper, the information-theoretic formulation of completion time is based on the concept of constrained rates, where users are allowed to employ different numbers of channel uses for transmission as opposed to the equal channel use of the standard information-theoretic formulation. Analogous to the capacity region, the completion time region characterizes all possible trade-offs among users' completion times. For a multi-access channel, it is shown that the completion time region is achieved by operating the channel in two independent phases: a multi-access phase when both users are transmitting, and a point-to-point phase when one user has finished and the other is still transmitting. Using a similar two-phase approach, the completion time region (or inner and outer bounds) is established for a Gaussian broadcast channel and a Gaussian interference channel. It is observed that although consisting of two convex subregions, the completion time region may not be convex in general. Finally an optimization problem of minimizing the weighted sum completion time for a Gaussian multi-access channel and a Gaussian broadcast channel is solved, demonstrating the utility of the completion time approach.
    Preview · Article · Aug 2015
  • Source
    Yuanpeng Liu · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a class of broadcast interference channels (BIC) is investigated, where one of the two broadcast receivers is subject to interference coming from a point-to-point transmission. For a general discrete memoryless broadcast interference channel (DM-BIC), an achievable scheme based on message splitting, superposition and binning is proposed and a concise representation of the corresponding achievable rate region R is obtained. Two partial-order broadcast conditions interference-oblivious less noisy and interference-cognizant less noisy are defined, thereby extending the usual less noisy condition for a regular broadcast channel by taking interference into account. Under these conditions, a reduced form of R is shown to be equivalent to a rate region based on a simpler scheme, where the broadcast transmitter uses only superposition. Furthermore, if interference is strong for the interference-oblivious less noisy DM-BIC, the capacity region is given by the aforementioned two equivalent rate regions. For a Gaussian broadcast interference channel (GBIC), channel parameters are categorized into three regimes. For the first two regimes, which are closely related to the two partial-order broadcast conditions, achievable rate regions are derived by specializing the corresponding achievable schemes of DM-BICs with Gaussian input distributions. The entropy power inequality (EPI) based outer bounds are obtained by combining bounding techniques for a Gaussian broadcast channel (GBC) and a Gaussian interference channel (GIC). These inner and outer bounds lead to either exact or approximate characterizations of capacity regions and sum capacity under various conditions. For the remaining complementing regime, inner and outer bounds are also provided.
    Preview · Article · Aug 2015 · IEEE Transactions on Information Theory
  • Source
    Oner Orhan · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: Energy harvesting multi-hop networks allow for perpetual operation of low cost, limited range wireless devices. Compared with their battery operated counterparts, the coupling of energy and data causality constraints with half duplex relay operation makes it challenging to operate such networks. In this paper, a throughput maximization problem for energy harvesting two-hop networks with decode-and-forward half-duplex relays is investigated. For a system with two parallel relays, various combinations of the following four transmission modes are considered: Broadcast from the source, multi-access from the relays, and successive relaying phases I and II. Optimal transmission policies for one and two parallel relays are studied under the assumption of non-causal knowledge of energy arrivals and finite size relay data buffers. The problem is formulated using a convex optimization framework, which allows for efficient numerical solutions and helps identify important properties of optimal policies. Numerical results are presented to provide throughput comparisons and to investigate the impact of multiple relays, size of relay data buffers, transmission modes, and energy harvesting on the throughput.
    Preview · Article · Jul 2015 · IEEE Journal on Selected Areas in Communications
  • R. Joda · E. Erkip · F. Lahouti
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, the problem of lossy source coding with side information at the decoder is considered when the dependency between the source and the side information (SI) is quasi-stationary and unknown to the encoder. This dependency is modeled using a (virtual) block fading channel. In order to help the decoder estimate the dependency, a part of the transmitted source in each block is coded at high rate (disregarding the SI) to be decoded error-free at the decoder. The estimate of the virtual block fading channel is imperfect and its quality depends on the length of the estimation block. The decoder's estimate is then quantized and communicated back to the encoder using a limited rate feedback. The encoder encodes the rest of the source block with this knowledge of the SI dependency model. A source coding scheme that uses the estimated dependency structure is proposed and the appropriate length of the source assigned for the estimation phase is characterized so as to minimize the mean distortion. The effect of the feedback rate, the quantization step size and the dependency estimation error are also investigated.
    No preview · Article · Jun 2015
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper studies noncoherent wideband systems with a single antenna transmitter and a multiple antenna receiver with many elements, under signaling with peak-to-average power ratio constraints. The analysis considers the scaling behavior of capacity and achievable rates by letting both the number of antennas and the bandwidth go to infinity jointly. In contrast to prior work on wideband single input single output (SISO) channels without a-priori channel state information, it is shown that a sufficiently large number of receive antennas can make up for the vanishingly small SNR at each antenna. In particular, it is shown that when bandwidth grows sufficiently slowly with the number of antennas, the capacity scaling with an increasing number of receive antennas is the same as the optimal coherent capacity scaling. If the bandwidth grows faster than a certain threshold, however, the additional bandwidth does not help because a finite transmit power is spread over an excessively large bandwidth.
    No preview · Article · Jun 2015
  • Source
    Roghayeh Joda · Farshad Lahouti · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper investigates delay-distortion-power trade offs in transmission of quasi-stationary sources over block fading channels by studying encoder and decoder buffering techniques to smooth out the source and channel variations. Four source and channel coding schemes that consider buffer and power constraints are presented to minimize the reconstructed source distortion. The first one is a high performance scheme, which benefits from optimized source and channel rate adaptation. In the second scheme, the channel coding rate is fixed and optimized along with transmission power with respect to channel and source variations; hence this scheme enjoys simplicity of implementation. The two last schemes have fixed transmission power with optimized adaptive or fixed channel coding rate. For all the proposed schemes, closed form solutions for mean distortion, optimized rate and power are provided and in the high SNR regime, the mean distortion exponent and the asymptotic mean power gains are derived. The proposed schemes with buffering exploit the diversity due to source and channel variations. Specifically, when the buffer size is limited, fixed channel rate adaptive power scheme outperforms an adaptive rate fixed power scheme. Furthermore, analytical and numerical results demonstrate that with limited buffer size, the system performance in terms of reconstructed signal SNR saturates as transmission power is increased, suggesting that appropriate buffer size selection is important to achieve a desired reconstruction quality.
    Full-text · Article · May 2015
  • [Show abstract] [Hide abstract]
    ABSTRACT: The papers in this special issue presents cutting-edge research results in the emerging area of energy harvesting wireless communications and wireless energy transfer. This first issue starts with a review article coauthored by the guest editors that summarizes recent results in the broad area of energy harvesting communications, in particular, in information-theoretic, offline and online schedulingtheoretic, medium access, networking approaches to energy harvesting communications, as well as in energy cooperation and simultaneous wireless energy and information transfer.
    No preview · Article · Mar 2015 · IEEE Journal on Selected Areas in Communications
  • Source
    Oner Orhan · Elza Erkip · Sundeep Rangan
    [Show abstract] [Hide abstract]
    ABSTRACT: The wide bandwidth and large number of antennas used in millimeter wave systems put a heavy burden on the power consumption at the receiver. In this paper, using an additive quantization noise model, the effect of analog-digital conversion (ADC) resolution and bandwidth on the achievable rate is investigated for a multi-antenna system under a receiver power constraint. Two receiver architectures, analog and digital combining, are compared in terms of performance. Results demonstrate that: (i) For both analog and digital combining, there is a maximum bandwidth beyond which the achievable rate decreases; (ii) Depending on the operating regime of the system, analog combiner may have higher rate but digital combining uses less bandwidth when only ADC power consumption is considered, (iii) digital combining may have higher rate when power consumption of all the components in the receiver front-end are taken into account.
    Preview · Article · Feb 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This article summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the information-theoretic performance limits to transmission scheduling policies and resource allocation, medium access and networking issues. The emerging related area of energy transfer for self-sustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed as well as models for energy consumption at the nodes.
    Preview · Article · Jan 2015 · IEEE Journal on Selected Areas in Communications
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Peaky and non-peaky signaling schemes have long been considered species apart in non-coherent wideband fading channels, as the first approaches asymptotically the linear-in-power capacity of a wideband AWGN channel with the same SNR, whereas the second reaches a nearly power-limited peak rate at some finite critical bandwidth and then falls to zero as bandwidth grows to infinity. In this paper it is shown that this distinction is in fact an artifact of the limited attention paid in the past to the product between the bandwidth and the fraction of time it is in use. This fundamental quantity, that is termed bandwidth occupancy, measures average bandwidth usage over time. As it turns out, a peaky signal that transmits in an infinite bandwidth but only for an infinitesimal fraction of the time may only have a small bandwidth occupancy, and so does a non-peaky scheme that limits itself to the critical bandwidth even though more spectrum is available, so as to not degrade rate. The two types of signaling in the literature are harmonized to show that, for any type of signals, there is a fundamental limit---a critical bandwidth occupancy. All signaling schemes with the same bandwidth occupancy approach the linear-in-power capacity of wideband AWGN channels with the same asymptotic behavior as the bandwidth occupancy approaches its critical value. For a bandwidth occupancy above the critical value, rate decreases to zero as the occupancy goes to infinity. This unified analysis not only recovers previous results on capacity bounds for (non-)peaky signaling schemes, but also reveals the fundamental tradeoff between accuracy and convergence when characterizing the maximal achievable rate.
    Full-text · Article · Jan 2015
  • Source
    Mustafa Anil Kocak · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: This work considers a communication scenario where the transmitter chooses a list of size K from a total of M messages to send over a noisy communication channel, the receiver generates a list of size L and communication is considered successful if the intersection of the lists at two terminals has cardinality greater than a threshold T. In traditional communication systems K=L=T=1. The fundamental limits of this setup in terms of K, L, T and the Shannon capacity of the channel between the terminals are examined. Specifically, necessary and/or sufficient conditions for asymptotically error free communication are provided.
    Preview · Article · Oct 2014
  • Source
    Oner Orhan · Deniz Gunduz · Elza Erkip
    [Show abstract] [Hide abstract]
    ABSTRACT: Source-channel coding for an energy limited wireless sensor node is investigated. The sensor node observes independent Gaussian source samples with variances changing over time slots and transmits to a destination over a flat fading channel. The fading is constant during each time slot. The compressed samples are stored in a finite size data buffer and need to be delivered in at most $d$ time slots. The objective is to design optimal transmission policies, namely, optimal power and distortion allocation, over the time slots such that the average distortion at destination is minimized. In particular, optimal transmission policies with various energy constraints are studied. First, a battery operated system in which sensor node has a finite amount of energy at the beginning of transmission is investigated. Then, the impact of energy harvesting, energy cost of processing and sampling are considered. For each energy constraint, a convex optimization problem is formulated, and the properties of optimal transmission policies are identified. For the strict delay case, $d=1$, $2D$ waterfilling interpretation is provided. Numerical results are presented to illustrate the structure of the optimal transmission policy, to analyze the effect of delay constraints, data buffer size, energy harvesting, processing and sampling costs.
    Preview · Article · Aug 2014 · IEEE Transactions on Wireless Communications
  • [Show abstract] [Hide abstract]
    ABSTRACT: In various wireless systems, such as sensor RFID networks and body area networks with implantable devices, the transmitted signals are simultaneously used both for information transmission and for energy transfer. In order to satisfy the conflicting requirements on information and energy transfer, this paper proposes the use of constrained run-length limited (RLL) codes in lieu of conventional unconstrained (i.e, random-like) capacity-achieving codes. The receiver's energy utilization requirements are modeled stochastically, and constraints are imposed on the probabilities of battery underflow and overflow at the receiver. It is demonstrated that the codewords' structure afforded by the use of constrained codes enables the transmission strategy to be better adjusted to the receiver's energy utilization pattern, as compared to classical unstructured codes. As a result, constrained codes allow a wider range of trade-offs between the rate of information transmission and the performance of energy transfer to be achieved.
    No preview · Conference Paper · Jun 2014
  • Source
    Osvaldo Simeone · Elza Erkip · Shlomo Shamai
    [Show abstract] [Hide abstract]
    ABSTRACT: The conventional design of cellular systems prescribes the separation of uplink and downlink transmissions via time-division or frequency-division duplex. Recent advances in analog and digital domain self-interference interference cancellation challenge the need for this arrangement and open up the possibility to operate base stations, especially low-power ones, in a full-duplex mode. As a means to cope with the resulting downlink-to-uplink interference among base stations, this letter investigates the impact of the Cloud Radio Access Network (C-RAN) architecture. The analysis follows an information theoretic approach based on the classical Wyner model. The analytical results herein confirm the significant potential advantages of the C-RAN architecture in the presence of full-duplex base stations, as long as sufficient fronthaul capacity is available and appropriate mobile station scheduling, or successive interference cancellation at the mobile stations, is implemented.
    Preview · Article · May 2014 · IEEE Wireless Communication Letters
  • O. Simeone · E. Erkip · S. Shamai
    [Show abstract] [Hide abstract]
    ABSTRACT: The conventional design of cellular systems prescribes the separation of uplink and downlink transmissions via time-division or frequency-division duplex. Recent advances in analog and digital domain self-interference interference cancellation challenge the need for this arrangement and open up the possibility to operate base stations, especially low-power ones, in a full-duplex mode. As a means to cope with the resulting downlink-to-uplink interference among base stations, this letter investigates the impact of the Cloud Radio Access Network (C-RAN) architecture. The analysis follows an information theoretic approach based on the classical Wyner model. The analytical results herein confirm the significant potential advantages of the C-RAN architecture in the presence of full-duplex base stations, as long as sufficient fronthaul capacity is available and appropriate mobile station scheduling, or successive interference cancellation at the mobile stations, is implemented.
    No preview · Article · Apr 2014
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: With millimeter wave bands emerging as a strong candidate for 5G cellular networks, next-generation systems may be in a unique position where spectrum is plentiful. To assess the potential value of this spectrum, this paper derives scaling laws on the per mobile downlink feasible rate with large bandwidth and number of nodes, for both Infrastructure Single Hop (ISH) and Infrastructure Multi-Hop (IMH) architectures. It is shown that, for both cases, there exist \emph{critical bandwidth scalings} above which increasing the bandwidth no longer increases the feasible rate per node. These critical thresholds coincide exactly with the bandwidths where, for each architecture, the network transitions from being degrees-of-freedom-limited to power-limited. For ISH, this critical bandwidth threshold is lower than IMH when the number of users per base station grows with network size. This result suggests that multi-hop transmissions may be necessary to fully exploit large bandwidth degrees of freedom in deployments with growing number of users per cell.
    Full-text · Conference Paper · Apr 2014
  • Source
    Zhili Guo · Yao Wang · Elza Erkip · Shivendra S. Panwar
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a cooperative multicast scheme that uses Randomized Distributed Space Time Codes (R-DSTC), along with packet level Forward Error Correction (FEC), is studied. Instead of sending source packets and/or parity packets through two hops using R-DSTC as proposed in our prior work, the new scheme delivers both source packets and parity packets using only one hop. After the source station (access point, AP) first sends all the source packets, the AP as well as all nodes that have received all source packets together send the parity packets using R-DSTC. As more parity packets are transmitted, more nodes can recover all source packets and join the parity packet transmission. The process continues until all nodes acknowledge the receipt of enough packets for recovering the source packets. For each given node distribution, the optimum transmission rates for source and parity packets are determined such that the video rate that can be sustained at all nodes is maximized. This new scheme can support significantly higher video rates, and correspondingly higher PSNR of decoded video, than the prior approaches. Three suboptimal approaches, which do not require full information about user distribution or the feedback, and hence are more feasible in practice are also presented. The proposed suboptimal scheme with only the node count information and without feedback still outperforms our prior approach that assumes full channel information and no feedback.
    Full-text · Article · Jan 2014 · IEEE Transactions on Multimedia
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Millimeter wave (mmW) frequencies between 30 and 300 GHz are a new frontier for cellular communication that offers the promise of orders of magnitude greater bandwidths combined with further gains via beamforming and spatial multiplexing from multi-element antenna arrays. This paper surveys measurements and capacity studies to assess this technology with a focus on small cell deployments in urban environments. The conclusions are extremely encouraging; measurements in New York City at 28 and 73 GHz demonstrate that, even in an urban canyon environment, significant non-line-of-sight (NLOS) outdoor, street-level coverage is possible up to approximately 200 m from a potential low power micro- or picocell base station. In addition, based on statistical channel models from these measurements, it is shown that mmW systems can offer more than an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks at current cell densities. Cellular systems, however, will need to be significantly redesigned to fully achieve these gains. Specifically, the requirement of highly directional and adaptive transmissions, directional isolation between links and significant possibilities of outage have strong implications on multiple access, channel structure, synchronization and receiver design. To address these challenges, the paper discusses how various technologies including adaptive beamforming, multihop relaying, heterogeneous network architectures and carrier aggregation can be leveraged in the mmW context.
    Full-text · Article · Jan 2014 · Proceedings of the IEEE
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: With the severe spectrum shortage in conventional cellular bands, millimeter wave (mmW) frequencies between 30 and 300 GHz have been attracting growing attention as a possible candidate for next-generation micro- and picocellular wireless networks. The mmW bands offer orders of magnitude greater spectrum than current cellular allocations and enable very high-dimensional antenna arrays for further gains via beamforming and spatial multiplexing. This paper uses recent real-world measurements at 28 and 73 GHz in New York City to derive detailed spatial statistical models of the channels and uses these models to provide a realistic assessment of mmW micro- and picocellular networks in a dense urban deployment. Statistical models are derived for key channel parameters including the path loss, number of spatial clusters, angular dispersion and blocking. It is found that, even in highly non-line-of-sight environments, strong signals can be detected 100m to 200m from potential cell sites, potentially with multiple clusters to support spatial multiplexing. Moreover, a system simulation based on the models predicts that mmW systems with cell radii of 100m can offer an order of magnitude increase in capacity over current state-of-the-art 4G cellular networks with similar cell density.
    Full-text · Article · Dec 2013 · IEEE Journal on Selected Areas in Communications

Publication Stats

13k Citations
183.68 Total Impact Points

Institutions

  • 2007-2015
    • Polytechnic Institute of New York University
      • Department of Electrical and Computer Engineering
      Brooklyn, New York, United States
  • 2013
    • Sabanci University
      İstanbul, Istanbul, Turkey
  • 2001-2013
    • City University of New York - Brooklyn College
      Brooklyn, New York, United States
  • 2008-2011
    • Worcester Polytechnic Institute
      • Department of Electrical and Computer Engineering
      Worcester, Massachusetts, United States
    • University of Naples Federico II
      Napoli, Campania, Italy
  • 2010
    • CTTC Catalan Telecommunications Technology Centre
      Barcino, Catalonia, Spain
  • 2009
    • New Jersey Institute of Technology
      • Department of Electrical and Computer Engineering
      Newark, NJ, United States
  • 2007-2009
    • Princeton University
      • Department of Electrical Engineering
      Princeton, NJ, United States
  • 1995-2007
    • Stanford University
      • • Department of Electrical Engineering
      • • Information Systems Laboratory
      Palo Alto, California, United States
  • 2005
    • CUNY Graduate Center
      New York City, New York, United States
    • Brooklyn Research
      New York City, New York, United States
  • 1997-2002
    • Rice University
      • Department of Electrical and Computer Engineering
      Houston, TX, United States