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20
A Power Efficient Sensing/Communication Scheme: Joint SourceChannelNetwork Coding by Using Compressive Sensing
"... Abstract—We propose a joint sourcechannelnetwork coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of ..."
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Abstract—We propose a joint sourcechannelnetwork coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint sourcechannel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomness of the network allows a mapping to lower dimensional spaces. Our approach relies on using analog random linear network coding. The receiver uses compressive sensing decoders to reconstruct sources. Our key insight is the fact that, compressive sensing and analog network coding both preserve the source characteristics required for compressive sensing decoding. I.
Algebraic Network Coding Approach to Deterministic Wireless Relay Networks
, 2010
"... Abstract—The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. Avestimehr et al. showed tha ..."
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Cited by 11 (2 self)
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Abstract—The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. Avestimehr et al. showed that the Mincut Maxflow theorem holds in the ADT network. In this paper, we show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Médard. We prove that the ADT network problem can be captured by a single matrix, called the system matrix. We show that the mincut of an ADT network is the rank of the system matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the mincut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections. Our algebraic approach not only provides the Mincut Maxflow theorem for a single unicast/multicast connection, but also extends to nonmulticast connections such as multiple multicast, disjoint multicast, and twolevel multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that the random linear network coding, a randomized distributed algorithm for network code construction, achieves capacity for the connections listed above. Finally, we extend the ADT networks to those with random erasures and cycles (thus, allowing bidirectional links). I.
MAC Design for Analog Network Coding
, 2010
"... Most medium access control mechanisms discard collided packets and consider interference harmful. Recent work on Analog Network Coding (ANC) suggests a different approach, in which multiple interfering transmissions are strategically scheduled. The received collisions are collected and then used in ..."
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Cited by 7 (3 self)
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Most medium access control mechanisms discard collided packets and consider interference harmful. Recent work on Analog Network Coding (ANC) suggests a different approach, in which multiple interfering transmissions are strategically scheduled. The received collisions are collected and then used in a decoding process, such as the ZigZag decoding process, where the packets involved in the collisions are extracted. In this paper, we present an algebraic representation of collisions and describe a general approach to recovering collisions using ANC. To study the effect of using ANC on the performance of MAC layers, we develop an ANCbased algorithm that implements an abstract MAC layer service, as defined in [1, 2], and analyze its performance. This study proves that ANC can significantly improve the performance of MAC layer services, in terms of probabilistic time guarantees for packet delivery. We illustrate how this improvement at the MAC layer can translate into faster higherlevel algorithms, by analyzing the time complexity of a multiplemessage networkwide broadcast algorithm that uses our ANCbased MAC service.
A Converse for the Wideband Relay Channel with Physically Degraded Broadcast
 IEEE INFORMATION THEORY WORKSHOP
, 2011
"... We investigate the multipath fading relay channel in the limit of a large bandwidth, and in the noncoherent setting, where the channel state is unknown to all terminals, including the relay and the destination. We derive a lower bound on the capacity by proposing and analyzing a peaky frequency bin ..."
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Cited by 6 (1 self)
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We investigate the multipath fading relay channel in the limit of a large bandwidth, and in the noncoherent setting, where the channel state is unknown to all terminals, including the relay and the destination. We derive a lower bound on the capacity by proposing and analyzing a peaky frequency binning scheme. The achievable rate obtained coincides with the blockMarkov lower bound on the capacity of the wideband frequencydivision Gaussian relay channel. When the broadcast channel is physically degraded, this achievable rate meets the cutset upperbound, and thus reaches the capacity of the noncoherent wideband multipath fading relay channel. In this case, a hypergraph model of the multipath fading relay channel is proposed, and the relaying scheme of concern is shown to reach its mincut. Even if the source treats the broadcast channel as physically degraded when it is stochastically degraded, the achievable hypergraph bound is the mincut.
Deterministic Network Model Revisited: An Algebraic Network Coding Approach
, 2010
"... The capacity of multiuser networks has been a longstanding problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature of wirele ..."
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Cited by 5 (1 self)
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The capacity of multiuser networks has been a longstanding problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate multiuser wireless networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless medium and interference. We show that the ADT network model can be described within the algebraic network coding framework introduced by Koetter and Médard. We prove that the ADT network problem can be captured by a single matrix, and show that the mincut of an ADT network is the rank of this matrix; thus, eliminating the need to optimize over exponential number of cuts between two nodes to compute the mincut of an ADT network. We extend the capacity characterization for ADT networks to a more general set of connections, including single unicast/multicast connection and nonmulticast connections such as multiple multicast, disjoint multicast, and twolevel multicast. We also provide sufficiency conditions for achievability in ADT networks for any general connection set. In addition, we show that random linear network coding, a randomized distributed algorithm for network code construction, achieves the capacity for the connections listed above. Furthermore, we extend the ADT networks to those with random erasures and cycles (thus, allowing bidirectional links). In addition, we propose an efficient linear code construction for the deterministic wireless multicast relay network model. Note that Avestimehr et al.’s proposed code construction is not guaranteed to be efficient and may potentially involve an infinite block length. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, for a layered network, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.
AmplifyandForward in Wireless Relay Networks
"... Abstract—A general class of wireless relay networks with a single sourcedestination pair is considered. Intermediate nodes in the network employ an amplifyandforward scheme to relay their input signals. In this case the overall inputoutput channel from the source via the relays to the destinatio ..."
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Cited by 5 (3 self)
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Abstract—A general class of wireless relay networks with a single sourcedestination pair is considered. Intermediate nodes in the network employ an amplifyandforward scheme to relay their input signals. In this case the overall inputoutput channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and signaltonoise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the achievable rate in amplifyandforward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplifyandforward schemes for some simple relay networks but also characterize the performance of such schemes in more complex relay networks which cannot be addressed in a straightforward manner with existing approaches. Using cutset arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplifyandforward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters. I.
Relays that cooperate to compute
 in Proc. Int. Symp. Wireless Commun. Syst
, 2012
"... Abstract—This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multipleaccess relay channel where two transmitters attempt to send the modulosum of their finite field messages to the receiver with the help of the relay. ..."
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Cited by 3 (2 self)
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Abstract—This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multipleaccess relay channel where two transmitters attempt to send the modulosum of their finite field messages to the receiver with the help of the relay. The transmitters use nested lattice codes to ensure that sums of codewords are protected against noise and to preserve the modulo operation of the finite field. We develop a block Markov coding scheme where the relay recovers the real sum of the codewords and retransmits it coherently with the two transmitters. I.
Scheduling Wireless Links with Successive Interference Cancellation
"... Abstract—In this paper we study the problem of scheduling wireless links in a model where successive interference cancellation is combined with the physical interference model and uniform power assignment. Successive interference cancellation is based on the observation that interfering signals shou ..."
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Cited by 2 (0 self)
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Abstract—In this paper we study the problem of scheduling wireless links in a model where successive interference cancellation is combined with the physical interference model and uniform power assignment. Successive interference cancellation is based on the observation that interfering signals should not be treated as random noise, but as wellstructured signals. By exploiting this structured nature, the strongest signal can be decoded and subtracted from a collision, thus enabling the decoding of weaker simultaneous signals. The procedure can be repeated iteratively as long as the collided signals differ in strength significantly. It has been shown that the problem of scheduling wireless links with successive interference cancellation is NPhard. In this work, we propose a polynomialtime scheduling algorithm that uses successive interference cancellation to compute short schedules for network topologies formed by nodes arbitrarily distributed in the Euclidean plane. We prove that the proposed algorithm is correct in the physical interference model and provide simulation results demonstrating the performance of the algorithm in different network topologies. We compare the results to solutions without successive interference cancellation and observe that throughput gains of up to 20 % are obtained in certain scenarios. I.
Analog Network Coding in General SNR Regime: Performance of A Greedy Scheme
"... Abstract—The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been c ..."
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Abstract—The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of the Gaussian Nrelay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. For general layered networks, our scheme allows us to compute optimal rates within a “small ” gap from the cutset upper bound asymptotically in the source power. I.
1Asymptotic Capacity and Optimal Precoding in MIMO MultiHop Relay Networks
"... Abstract—A multihop relaying system is analyzed where data sent by a multiantenna source is relayed by successive multiantenna relays until it reaches a multiantenna destination. Assuming correlated fading at each hop, each relay receives a faded version of the signal from the previous level, pe ..."
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Abstract—A multihop relaying system is analyzed where data sent by a multiantenna source is relayed by successive multiantenna relays until it reaches a multiantenna destination. Assuming correlated fading at each hop, each relay receives a faded version of the signal from the previous level, performs linear precoding and retransmits it to the next level. Using free probability theory and assuming that the noise power at relays— but not at destination — is negligible, the closedform expression of the asymptotic instantaneous endtoend mutual information is derived as the number of antennas at all levels grows large. The soobtained deterministic expression is independent from the channel realizations while depending only on channel statistics. This expression is also shown to be equal to the asymptotic average endtoend mutual information. The singular vectors of the optimal precoding matrices, maximizing the average mutual information with finite number of antennas at all levels, are also obtained. It turns out that these vectors are aligned to the eigenvectors of the channel correlation matrices. Thus they can be determined using only the channel statistics. As the structure of the singular vectors of the optimal precoders is independent from the system size, it is also optimal in the asymptotic regime. Index Terms—asymptotic capacity, correlated channel, free probability theory, multihop relay network, precoding. I.