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A. Salman Avestimehr

Publications and source records attributed to A. Salman Avestimehr.

80 records · Page 5Linked to original sources
arXiv2012

Diamond Networks with Bursty Traffic: Bounds on the Minimum Energy-Per-Bit

When data traffic in a wireless network is bursty, small amounts of data sporadically become available for transmission, at times that are unknown at the receivers, and an extra amount of energy must be spent at the transmitters to overcome this lack of synchronization between the network nodes. In practice, pre-defined header sequences are used with the purpose of synchronizing the different network nodes. However, in networks where relays must be used for communication, the overhead required for synchronizing the entire network may be very significant. In this work, we study the fundamental limits of energy-efficient communication in an asynchronous diamond network with two relays. We formalize the notion of relay synchronization by saying that a relay is synchronized if the conditional entropy of the arrival time of the source message given the received signals at the relay is small. We show that the minimum energy-per-bit for bursty traffic in diamond networks is achieved with a coding scheme where each relay is either synchronized or not used at all. A consequence of this result is the derivation of a lower bound to the minimum energy-per-bit for bursty communication in diamond networks. This bound allows us to show that schemes that perform the tasks of synchronization and communication separately (i.e., with synchronization signals preceding the communication block) can achieve the minimum energy-per-bit to within a constant fraction that ranges from 2 in the synchronous case to 1 in the highly asynchronous regime.

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arXiv2011

Divide-and-conquer: Approaching the capacity of the two-pair bidirectional Gaussian relay network

The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or half-duplex mode for arbitrary number of pairs is characterized. It is shown that the cut-set upper-bound is tight and the capacity region is achieved by a so called divide-and-conquer relaying strategy. The insights gained from the deterministic network are then used for the Gaussian bidirectional relay network. The strategy in the deterministic channel translates to a specific superposition of lattice codes and random Gaussian codes at the source nodes and successive interference cancelation at the receiving nodes for the Gaussian network. The achievable rate of this scheme with two pairs is analyzed and it is shown that for all channel gains it achieves to within 3 bits/sec/Hz per user of the cut-set upper-bound. Hence, the capacity region of the two-pair bidirectional Gaussian relay network to within 3 bits/sec/Hz per user is characterized.

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arXiv2011

Improving the Thresholds of Sparse Recovery: An Analysis of a Two-Step Reweighted Basis Pursuit Algorithm

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions, so that with high probability almost all sparse signals can be recovered from i.i.d. Gaussian measurements, have been computed and are referred to as "weak thresholds" \cite{D}. In this paper, we introduce a reweighted $\ell_1$ recovery algorithm composed of two steps: a standard $\ell_1$ minimization step to identify a set of entries where the signal is likely to reside, and a weighted $\ell_1$ minimization step where entries outside this set are penalized. For signals where the non-sparse component entries are independent and identically drawn from certain classes of distributions, (including most well known continuous distributions), we prove a \emph{strict} improvement in the weak recovery threshold. Our analysis suggests that the level of improvement in the weak threshold depends on the behavior of the distribution at the origin. Numerical simulations verify the distribution dependence of the threshold improvement very well, and suggest that in the case of i.i.d. Gaussian nonzero entries, the improvement can be quite impressive---over 20% in the example we consider.

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arXiv2011

On the Sum-Capacity with Successive Decoding in Interference Channels

In this paper, we investigate the sum-capacity of the two-user Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sum-capacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sum-capacity oscillates as a function of the cross link gain parameters between the information theoretic sum-capacity and the sum-capacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sum-capacity, the maximum achievable sum-rate drops to that with interference treated as noise. We provide two algorithms (a simple one and a finer one) to translate the optimal schemes in the deterministic channel model to the Gaussian channel model. We also derive two upper bounds on the sum-capacity of the Gaussian Han-Kobayashi schemes, which automatically upper bound the sum-capacity using successive decoding of Gaussian codewords. Numerical evaluations show that, similar to the deterministic channel results, the constrained sum-capacity in the Gaussian channels oscillates between the sum-capacity with Han-Kobayashi schemes and that with single message schemes.

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arXiv2010

On Achieving Local View Capacity Via Maximal Independent Graph Scheduling

"If we know more, we can achieve more." This adage also applies to communication networks, where more information about the network state translates into higher sumrates. In this paper, we formalize this increase of sum-rate with increased knowledge of the network state. The knowledge of network state is measured in terms of the number of hops, h, of information available to each transmitter and is labeled as h-local view. To understand how much capacity is lost due to limited information, we propose to use the metric of normalized sum-capacity, which is the h-local view sum-capacity divided by global-view sum capacity. For the cases of one and two-local view, we characterize the normalized sum-capacity for many classes of deterministic and Gaussian interference networks. In many cases, a scheduling scheme called maximal independent graph scheduling is shown to achieve normalized sum-capacity. We also show that its generalization for 1-local view, labeled coded set scheduling, achieves normalized sum-capacity in some cases where its uncoded counterpart fails to do so.

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arXiv2010

Analyzing Weighted $\ell_1$ Minimization for Sparse Recovery with Nonuniform Sparse Models\footnote{The results of this paper were presented in part at the International Symposium on Information Theory, ISIT 2009}

In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted $\ell_1$ minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into two sets, with entries of each set having a specific probability of being nonzero. We propose a weighted $\ell_1$ minimization recovery algorithm and analyze its performance using a Grassmann angle approach. We compute explicitly the relationship between the system parameters-the weights, the number of measurements, the size of the two sets, the probabilities of being nonzero- so that when i.i.d. random Gaussian measurement matrices are used, the weighted $\ell_1$ minimization recovers a randomly selected signal drawn from the considered sparsity model with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We demonstrate through rigorous analysis and simulations that for the case when the support of the signal can be divided into two different subclasses with unequal sparsity fractions, the optimal weighted $\ell_1$ minimization outperforms the regular $\ell_1$ minimization substantially. We also generalize the results to an arbitrary number of classes.

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arXiv2010

The Two-User Deterministic Interference Channel with Rate-Limited Feedback

In this paper we study the effect of rate-limited feedback on the sum-rate capacity of the deterministic interference channel. We characterize the sum-rate capacity of this channel in the symmetric case and show that having feedback links can increase the sum-rate capacity by at most the rate of the available feedback. Our proof includes a novel upper-bound on the sum-rate capacity and a set of new achievability strategies.

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