arXiv subjects

Hesham El Gamal

Publications and source records attributed to Hesham El Gamal.

64 records · Page 4Linked to original sources

arXiv2006

On the Secrecy Capacity of Fading Channels

We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner's wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a low-complexity on/off power allocation strategy that achieves near-optimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels.

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arXiv2006

ARQ Diversity in Fading Random Access Channels

A cross-layer optimization approach is adopted for the design of symmetric random access wireless systems. Instead of the traditional collision model, a more realistic physical layer model is considered. Based on this model, an Incremental Redundancy Automatic Repeat reQuest (IR-ARQ) scheme, tailored to jointly combat the effects of collisions, multi-path fading, and additive noise, is developed. The Diversity-Multiplexing-Delay tradeoff (DMDT) of the proposed scheme is analyzed for fully-loaded queues, and compared with that of Gallager tree algorithm for collision resolution and the network-assisted diversity multiple access (NDMA) protocol of Tsatsanis et al.. The fully-loaded queue model is then replaced by one with random arrivals, under which these protocols are compared in terms of the stability region, average delay and diversity gain. Overall, our analytical and numerical results establish the superiority of the proposed IR-ARQ scheme and reveal some important insights. For example, it turns out that the performance is optimized, for a given total throughput, by maximizing the probability that a certain user sends a new packet and minimizing the transmission rate employed by each user.

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arXiv2006

Cooperative Lattice Coding and Decoding

A novel lattice coding framework is proposed for outage-limited cooperative channels. This framework provides practical implementations for the optimal cooperation protocols proposed by Azarian et al. In particular, for the relay channel we implement a variant of the dynamic decode and forward protocol, which uses orthogonal constellations to reduce the channel seen by the destination to a single-input single-output time-selective one, while inheriting the same diversity-multiplexing tradeoff. This simplification allows for building the receiver using traditional belief propagation or tree search architectures. Our framework also generalizes the coding scheme of Yang and Belfiore in the context of amplify and forward cooperation. For the cooperative multiple access channel, a tree coding approach, matched to the optimal linear cooperation protocol of Azarain et al, is developed. For this scenario, the MMSE-DFE Fano decoder is shown to enjoy an excellent tradeoff between performance and complexity. Finally, the utility of the proposed schemes is established via a comprehensive simulation study.

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arXiv2006

On the Optimality of the ARQ-DDF Protocol

The performance of the automatic repeat request-dynamic decode and forward (ARQ-DDF) cooperation protocol is analyzed in two distinct scenarios. The first scenario is the multiple access relay (MAR) channel where a single relay is dedicated to simultaneously help several multiple access users. For this setup, it is shown that the ARQ-DDF protocol achieves the optimal diversity multiplexing tradeoff (DMT) of the channel. The second scenario is the cooperative vector multiple access (CVMA) channel where the users cooperate in delivering their messages to a destination equipped with multiple receiving antennas. For this setup, we develop a new variant of the ARQ-DDF protocol where the users are purposefully instructed not to cooperate in the first round of transmission. Lower and upper bounds on the achievable DMT are then derived. These bounds are shown to converge to the optimal tradeoff as the number of transmission rounds increases.

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arXiv2005

The Water-Filling Game in Fading Multiple Access Channels

We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding water-filling game. This result sheds a new light on the opportunistic communication principle and argues for the fairness of the sum-rate optimal point, at least from a game theoretic perspective. The base-station is then introduced as a player interested in maximizing a weighted sum of the individual rates. We propose a Stackelberg formulation in which the base-station is the designated game leader. In this set-up, the base-station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sum-rate optimal point. On the negative side, we prove the non-existence of a base-station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, we present a repeated game approach which achieves the capacity region of the fading multiple access channel. Finally, we extend our study to vector channels highlighting interesting differences between this scenario and the scalar channel case.

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arXiv2005

The Throughput-Reliability Tradeoff in MIMO Channels

In this paper, an outage limited MIMO channel is considered. We build on Zheng and Tse's elegant formulation of the diversity-multiplexing tradeoff to develop a better understanding of the asymptotic relationship between the probability of error, transmission rate, and signal-to-noise ratio. In particular, we identify the limitation imposed by the multiplexing gain notion and develop a new formulation for the throughput-reliability tradeoff that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of MIMO channels.

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arXiv2005

The Three Node Wireless Network: Achievable Rates and Cooperation Strategies

We consider a wireless network composed of three nodes and limited by the half-duplex and total power constraints. This formulation encompasses many of the special cases studied in the literature and allows for capturing the common features shared by them. Here, we focus on three special cases, namely 1) Relay Channel, 2) Multicast Channel, and 3) Conference Channel. These special cases are judicially chosen to reflect varying degrees of complexity while highlighting the common ground shared by the different variants of the three node wireless network. For the relay channel, we propose a new cooperation scheme that exploits the wireless feedback gain. This scheme combines the benefits of decode-and-forward and compress-and-forward strategies and avoids the idealistic feedback assumption adopted in earlier works. Our analysis of the achievable rate of this scheme reveals the diminishing feedback gain at both the low and high signal-to-noise ratio regimes. Inspired by the proposed feedback strategy, we identify a greedy cooperation framework applicable to both the multicast and conference channels. Our performance analysis reveals several nice properties of the proposed greedy approach and the central role of cooperative source-channel coding in exploiting the receiver side information in the wireless network setting. Our proofs for the cooperative multicast with side-information rely on novel nested and independent binning encoders along with a list decoder.

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arXiv2005

A Unified Framework for Tree Search Decoding : Rediscovering the Sequential Decoder

We consider receiver design for coded transmission over linear Gaussian channels. We restrict ourselves to the class of lattice codes and formulate the joint detection and decoding problem as a closest lattice point search (CLPS). Here, a tree search framework for solving the CLPS is adopted. In our framework, the CLPS algorithm decomposes into the preprocessing and tree search stages. The role of the preprocessing stage is to expose the tree structure in a form {\em matched} to the search stage. We argue that the minimum mean square error decision feedback (MMSE-DFE) frontend is instrumental for solving the joint detection and decoding problem in a single search stage. It is further shown that MMSE-DFE filtering allows for using lattice reduction methods to reduce complexity, at the expense of a marginal performance loss, and solving under-determined linear systems. For the search stage, we present a generic method, based on the branch and bound (BB) algorithm, and show that it encompasses all existing sphere decoders as special cases. The proposed generic algorithm further allows for an interesting classification of tree search decoders, sheds more light on the structural properties of all known sphere decoders, and inspires the design of more efficient decoders. In particular, an efficient decoding algorithm that resembles the well known Fano sequential decoder is identified. The excellent performance-complexity tradeoff achieved by the proposed MMSE-Fano decoder is established via simulation results and analytical arguments in several MIMO and ISI scenarios.

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arXiv2005

On the Achievable Diversity-Multiplexing Tradeoffs in Half-Duplex Cooperative Channels

In this paper, we propose novel cooperative transmission protocols for delay limited coherent fading channels consisting of N (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (up-link) channels. For the relay channel, we investigate two classes of cooperation schemes; namely, Amplify and Forward (AF) protocols and Decode and Forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with N-1 relays where it is shown to outperform the space-time coded protocol of Laneman and Worenell without requiring decoding/encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains 0 < r < 1/N. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the cooperative multiple-access channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the sub-optimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint.

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arXiv2005

On the Throughput-Delay Tradeoff in Cellular Multicast

In this paper, we adopt a cross layer design approach for analyzing the throughput-delay tradeoff of the multicast channel in a single cell system. To illustrate the main ideas, we start with the single group case, i.e., pure multicast, where a common information stream is requested by all the users. We consider three classes of scheduling algorithms with progressively increasing complexity. The first class strives for minimum complexity by resorting to a static scheduling strategy along with memoryless decoding. Our analysis for this class of scheduling algorithms reveals the existence of a static scheduling policy that achieves the optimal scaling law of the throughput at the expense of a delay that increases exponentially with the number of users. The second scheduling policy resorts to a higher complexity incremental redundancy encoding/decoding strategy to achieve a superior throughput-delay tradeoff. The third, and most complex, scheduling strategy benefits from the cooperation between the different users to minimize the delay while achieving the optimal scaling law of the throughput. In particular, the proposed cooperative multicast strategy is shown to simultaneously achieve the optimal scaling laws of both throughput and delay. Then, we generalize our scheduling algorithms to exploit the multi-group diversity available when different information streams are requested by different subsets of the user population. Finally, we discuss the effect of the potential gains of equipping the base station with multi-transmit antennas and present simulation results that validate our theoretical claims.

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