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21
On the Capacity of the Finite Field Counterparts of Wireless Interference Networks
, 2013
"... This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous ..."
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This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity or linear capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over Fpn are analogous to n × n vector (MIMO) channels in the wireless setting, but with an important distinction – there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity or linear capacity optimal solutions for their finite field counterparts. This is shown through the study of capacity of the 2user X channel and linear capacity of the 3user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over Fpn also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.
On Interference Alignment and the Deterministic Capacity for Cellular Channels with Weak Symmetric Cross Links
 in Proc. IEEE Int. Symp. on Information Theory (ISIT), Saint
, 2011
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On the Optimality of Treating Interference as Noise for K user Parallel Gaussian Interference Networks
"... It has been shown recently by Geng et al. that in a K user Gaussian interference network, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all signal strengths measured in ..."
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It has been shown recently by Geng et al. that in a K user Gaussian interference network, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all signal strengths measured in dB scale), then power control and treating interference as noise (TIN) is sufficient to achieve the entire generalized degrees of freedom (GDoF) region. Motivated by the intuition that the deterministic model of Avestimehr et al. (ADT deterministic model) is particularly suited for exploring the optimality of TIN, the results of Geng et al. are first revisited under the ADT deterministic model, and are shown to directly translate between the Gaussian and deterministic settings. Next, we focus on the extension of these results to parallel interference networks, from a sumcapacity/sumGDoF perspective. To this end, we interpret the explicit characterization of the sumcapacity/sumGDoF of a TIN optimal network (without parallel channels) as a minimum weighted matching problem in combinatorial optimization, and obtain a simple characterization in terms of a partition of the interference network into vertexdisjoint cycles. Aided by insights from the cyclic partition, the sumcapacity optimality of TIN for K user parallel interference networks is characterized for the ADT deterministic model, leading ultimately to corresponding GDoF results for the Gaussian setting. In both cases, subject to a mild invertibility condition the optimality of TIN is shown to extend to parallel networks in a separable fashion.
On the Optimality of Treating Interference as Noise: General Message Sets
"... Abstract — In a Kuser Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating int ..."
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Abstract — In a Kuser Gaussian interference channel, it has been shown that if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in decibel scale), then treating interference as noise (TIN) is optimal from the perspective of generalized degrees of freedom (GDoF) and achieves the entire channel capacity region to within a constant gap. In this paper, we show that for such TINoptimal interference channels, even if the message set is expanded to include an independent message from each transmitter to each receiver, operating the new channel as the original interference channel and treating interference as noise is still optimal for the sum capacity up to a constant gap. Furthermore, we extend the result to the sumGDoF optimality of TIN in the general setting of X channels with arbitrary numbers of transmitters and receivers. Index Terms — Gaussian networks, generalized degrees of freedom (GDoF), sum capacity, treating interference as noise (TIN), X channels. I.
Optimum Transmission Strategies for the Gaussian OnetoMany Interference Network
"... Abstract—We study the Gaussian onetomany interference network which is obtained as a special case of a general interference network, where only one transmitter generates interference in the network. We allow transmission of messages on all the links of the network. This communication model is dif ..."
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Abstract—We study the Gaussian onetomany interference network which is obtained as a special case of a general interference network, where only one transmitter generates interference in the network. We allow transmission of messages on all the links of the network. This communication model is different from the corresponding onetomany interference channel. We formulate two transmission strategies for the above network, which involve using Gaussian codebooks and treating interference as noise at a subset of the receivers. We use sumrate as the criterion of optimality for evaluating the strategies. For the first strategy, we characterize the sumrate capacity under certain channel conditions, while for the second strategy, we derive a sumrate outer bound and characterize the gap between the outer bound and the achievable sumrate of the strategy. Next, we show that the solution approach for the second strategy has applications to the cascade Gaussian Z network, a network consisting of parallel pointtopoint links, where each transmitter except the last has a communication link to the adjacent receiver. Lastly, we illustrate the regions corresponding to the derived channel conditions for each strategy.
MIMO Gaussian X Channel: Noisy Interference Regime
"... Abstract—The twouser multipleinput multipleoutput (MIMO) Gaussian X channel (XC) consists of two transmitters and two receivers, with each transmitter having an independent message to each receiver. The sum capacity of the twouser MIMO Gaussian XC is determined in a noisy interference regime. Th ..."
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Abstract—The twouser multipleinput multipleoutput (MIMO) Gaussian X channel (XC) consists of two transmitters and two receivers, with each transmitter having an independent message to each receiver. The sum capacity of the twouser MIMO Gaussian XC is determined in a noisy interference regime. This sum capacity is achieved by using Gaussian codebooks for the messages on both the direct links (or both the cross links) and treating the interference from the cross links (or direct links) as noise. Index Terms—Interference channel, X channel, sum capacity, MIMO. I.
On the Symmetric 2User Deterministic Interference Channel with Confidential Messages
"... Abstract—We consider 2user symmetric interference channels with confidential messages. For the linear deterministic model of this channel, we develop inner and outer bounds for the symmetric secure rate, which are shown to match and characterize the symmetric secure capacity for a wide range of ch ..."
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Abstract—We consider 2user symmetric interference channels with confidential messages. For the linear deterministic model of this channel, we develop inner and outer bounds for the symmetric secure rate, which are shown to match and characterize the symmetric secure capacity for a wide range of channel parameters. For the achievability, we present a cooperative jamming scheme based on interference alignment principle, which is optimal for all regimes where the symmetric secure capacity is established. For the converse, a tighter outer bound than all perviously existing ones is provided for the regime where the symmetric secure capacity is still open. I.
Transmitter Cooperation under Finite Precision CSIT: A GDoF Perspective
"... Abstract—The benefits of partial and full transmitter cooperation are evaluated for a two user interference channel under finite precision channel state information at the transmitters (CSIT), using the generalized degrees of freedom (GDoF) metric. Under finite precision CSIT, the benefits of inter ..."
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Abstract—The benefits of partial and full transmitter cooperation are evaluated for a two user interference channel under finite precision channel state information at the transmitters (CSIT), using the generalized degrees of freedom (GDoF) metric. Under finite precision CSIT, the benefits of interference alignment are completely lost, so that the X channel obtained by partial transmitter cooperation does no better than the underlying interference channels. Full transmitter cooperation produces a vector broadcast channel (BC) which has a strict GDoF advantage over partial cooperation (X channel) and whose GDoF are fully achieved by interference enhancement. I.
IEEE TRANSACTIONS ON INFORMATION THEORY 1 On the Gaussian ManytoOne X Channel
"... Abstract—In this paper, the Gaussian manytoone X channel, which is a special case of general multiuser X channel, is studied. In the Gaussian manytoone X channel, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter ..."
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Abstract—In this paper, the Gaussian manytoone X channel, which is a special case of general multiuser X channel, is studied. In the Gaussian manytoone X channel, communication links exist between all transmitters and one of the receivers, along with a communication link between each transmitter and its corresponding receiver. As per the X channel assumption, transmission of messages is allowed on all the links of the channel. This communication model is different from the corresponding manytoone interference channel (IC). Transmission strategies which involve using Gaussian codebooks and treating interference from a subset of transmitters as noise are formulated for the above channel. Sumrate is used as the criterion of optimality for evaluating the strategies. Initially, a 3×3 manytoone X channel is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sumrate capacity under certain channel conditions. For the third strategy, a sumrate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the K ×K case. Next, a region in which the manytoone X channel can be operated as a manytoone IC without loss of sumrate is identified. Further, in the above region, it is shown that using Gaussian codebooks and treating interference as noise achieves a rate point that is within K/2 − 1 bits from the sumrate capacity. Subsequently, some implications of the above results to the Gaussian manytoone IC are discussed. Transmission strategies for the manytoone IC are formulated and channel conditions under which the strategies achieve sumrate capacity are obtained. A region where the sumrate capacity can be characterized to within K/2 − 1 bits is also identified. Finally, the regions where the derived channel conditions are satisfied for each strategy are illustrated for a 3×3 manytoone X channel and the corresponding manytoone IC. Index Terms—Interference channel, manytoone interference channel, sum capacity, X channel. I.
ISRO Satellite Center
"... Abstract—In this paper, we analyze the Gaussian X channel in the mixed interference regime. In this regime, multiple access transmission to one of the receivers is shown to be close to optimal in terms of sum rate. Three upper bounds are derived for the sum capacity in the mixed interference regime, ..."
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Abstract—In this paper, we analyze the Gaussian X channel in the mixed interference regime. In this regime, multiple access transmission to one of the receivers is shown to be close to optimal in terms of sum rate. Three upper bounds are derived for the sum capacity in the mixed interference regime, and the subregions where each of these bounds dominate the others are identified. The genieaided sum capacity upper bounds derived also show that the gap between sum capacity and the sum rate of the multiple access transmission scheme is small for a significant part of the mixed interference region. For any δ> 0, the region where multiple access transmission to one of the receivers is within δ from sum capacity is determined. Keywords—Gaussian X channel, sum capacity, mixed interference, genieaided bound, multiple access I. INTRODUCTION AND PROBLEM STATEMENT