arXiv subjects

Changho Suh

Publications and source records attributed to Changho Suh.

At least 37 records · Page 2Linked to original sources

arXiv2016

Information Recovery from Pairwise Measurements

This paper is concerned with jointly recovering $n$ node-variables $\left\{ x_{i}\right\}_{1\leq i\leq n}$ from a collection of pairwise difference measurements. Imagine we acquire a few observations taking the form of $x_{i}-x_{j}$; the observation pattern is represented by a measurement graph $\mathcal{G}$ with an edge set $\mathcal{E}$ such that $x_{i}-x_{j}$ is observed if and only if $(i,j)\in\mathcal{E}$. To account for noisy measurements in a general manner, we model the data acquisition process by a set of channels with given input/output transition measures. Employing information-theoretic tools applied to channel decoding problems, we develop a \emph{unified} framework to characterize the fundamental recovery criterion, which accommodates general graph structures, alphabet sizes, and channel transition measures. In particular, our results isolate a family of \emph{minimum} \emph{channel divergence measures} to characterize the degree of measurement corruption, which together with the size of the minimum cut of $\mathcal{G}$ dictates the feasibility of exact information recovery. For various homogeneous graphs, the recovery condition depends almost only on the edge sparsity of the measurement graph irrespective of other graphical metrics; alternatively, the minimum sample complexity required for these graphs scales like \[ \text{minimum sample complexity }\asymp\frac{n\log n}{\mathsf{Hel}_{1/2}^{\min}} \] for certain information metric $\mathsf{Hel}_{1/2}^{\min}$ defined in the main text, as long as the alphabet size is not super-polynomial in $n$. We apply our general theory to three concrete applications, including the stochastic block model, the outlier model, and the haplotype assembly problem. Our theory leads to order-wise tight recovery conditions for all these scenarios.

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arXiv2016

Role of a Relay in Bursty Multiple Access Channels

We investigate the role of a relay in multiple access channels (MACs) with bursty user traffic, where intermittent data traffic restricts the users to bursty transmissions. As our main result, we characterize the degrees of freedom (DoF) region of a $K$-user bursty multi-input multi-output (MIMO) Gaussian MAC with a relay, where Bernoulli random states are introduced to govern bursty user transmissions. To that end, we extend the noisy network coding scheme to achieve the cut-set bound. Our main contribution is in exploring the role of a relay from various perspectives. First, we show that a relay can provide a DoF gain in bursty channels, unlike in conventional non-bursty channels. Interestingly, we find that the relaying gain can scale with additional antennas at the relay to some extent. Moreover, observing that a relay can help achieve collision-free performances, we establish the necessary and sufficient condition for attaining collision-free DoF. Lastly, we consider scenarios in which some physical perturbation shared around the users may generate data traffic simultaneously, causing transmission patterns across them to be correlated. We demonstrate that for most cases in such scenarios, the relaying gain is greater when the users' transmission patterns are more correlated, hence when more severe collisions take place. Our results have practical implications in various scenarios of wireless networks such as device-to-device systems and random media access control protocols.

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arXiv2016

Top-$K$ Ranking from Pairwise Comparisons: When Spectral Ranking is Optimal

We explore the top-$K$ rank aggregation problem. Suppose a collection of items is compared in pairs repeatedly, and we aim to recover a consistent ordering that focuses on the top-$K$ ranked items based on partially revealed preference information. We investigate the Bradley-Terry-Luce model in which one ranks items according to their perceived utilities modeled as noisy observations of their underlying true utilities. Our main contributions are two-fold. First, in a general comparison model where item pairs to compare are given a priori, we attain an upper and lower bound on the sample size for reliable recovery of the top-$K$ ranked items. Second, more importantly, extending the result to a random comparison model where item pairs to compare are chosen independently with some probability, we show that in slightly restricted regimes, the gap between the derived bounds reduces to a constant factor, hence reveals that a spectral method can achieve the minimax optimality on the (order-wise) sample size required for top-$K$ ranking. That is to say, we demonstrate a spectral method alone to be sufficient to achieve the optimality and advantageous in terms of computational complexity, as it does not require an additional stage of maximum likelihood estimation that a state-of-the-art scheme employs to achieve the optimality. We corroborate our main results by numerical experiments.

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arXiv2016

Computation in Multicast Networks: Function Alignment and Converse Theorems

The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an identical function of the original messages. For a countably infinite class of two-transmitter two-receiver single-hop linear deterministic networks, the computing capacity is characterized for a linear function (modulo-2 sum) of Bernoulli sources. Inspired by the geometric concept of interference alignment in networks, a new achievable coding scheme called function alignment is introduced. A new converse theorem is established that is tighter than cut-set based and genie-aided bounds. Computation (vs. communication) over multicast networks requires additional analysis to account for multiple receivers sharing a network's computational resources. We also develop a network decomposition theorem which identifies elementary parallel subnetworks that can constitute an original network without loss of optimality. The decomposition theorem provides a conceptually-simpler algebraic proof of achievability that generalizes to $L$-transmitter $L$-receiver networks.

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arXiv2016

Adversarial Top-$K$ Ranking

We study the top-$K$ ranking problem where the goal is to recover the set of top-$K$ ranked items out of a large collection of items based on partially revealed preferences. We consider an adversarial crowdsourced setting where there are two population sets, and pairwise comparison samples drawn from one of the populations follow the standard Bradley-Terry-Luce model (i.e., the chance of item $i$ beating item $j$ is proportional to the relative score of item $i$ to item $j$), while in the other population, the corresponding chance is inversely proportional to the relative score. When the relative size of the two populations is known, we characterize the minimax limit on the sample size required (up to a constant) for reliably identifying the top-$K$ items, and demonstrate how it scales with the relative size. Moreover, by leveraging a tensor decomposition method for disambiguating mixture distributions, we extend our result to the more realistic scenario in which the relative population size is unknown, thus establishing an upper bound on the fundamental limit of the sample size for recovering the top-$K$ set.

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arXiv2015

Euclidean Information Theory of Networks

In this paper, we extend the information theoretic framework that was developed in earlier work to multi-hop network settings. For a given network, we construct a novel deterministic model that quantifies the ability of the network in transmitting private and common messages across users. Based on this model, we formulate a linear optimization problem that explores the throughput of a multi-layer network, thereby offering the optimal strategy as to what kind of common messages should be generated in the network to maximize the throughput. With this deterministic model, we also investigate the role of feedback for multi-layer networks, from which we identify a variety of scenarios in which feedback can improve transmission efficiency. Our results provide fundamental guidelines as to how to coordinate cooperation between users to enable efficient information exchanges across them.

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arXiv2015

Spectral MLE: Top-$K$ Rank Aggregation from Pairwise Comparisons

This paper explores the preference-based top-$K$ rank aggregation problem. Suppose that a collection of items is repeatedly compared in pairs, and one wishes to recover a consistent ordering that emphasizes the top-$K$ ranked items, based on partially revealed preferences. We focus on the Bradley-Terry-Luce (BTL) model that postulates a set of latent preference scores underlying all items, where the odds of paired comparisons depend only on the relative scores of the items involved. We characterize the minimax limits on identifiability of top-$K$ ranked items, in the presence of random and non-adaptive sampling. Our results highlight a separation measure that quantifies the gap of preference scores between the $K^{\text{th}}$ and $(K+1)^{\text{th}}$ ranked items. The minimum sample complexity required for reliable top-$K$ ranking scales inversely with the separation measure irrespective of other preference distribution metrics. To approach this minimax limit, we propose a nearly linear-time ranking scheme, called \emph{Spectral MLE}, that returns the indices of the top-$K$ items in accordance to a careful score estimate. In a nutshell, Spectral MLE starts with an initial score estimate with minimal squared loss (obtained via a spectral method), and then successively refines each component with the assistance of coordinate-wise MLEs. Encouragingly, Spectral MLE allows perfect top-$K$ item identification under minimal sample complexity. The practical applicability of Spectral MLE is further corroborated by numerical experiments.

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arXiv2015

A Relay Can Increase Degrees of Freedom in Bursty Interference Networks

We investigate the benefits of relays in multi-user wireless networks with bursty user traffic, where intermittent data traffic restricts the users to bursty transmissions. To this end, we study a two-user bursty MIMO Gaussian interference channel with a relay, where two Bernoulli random states govern the bursty user traffic. We show that an in-band relay can provide a degrees of freedom (DoF) gain in this bursty channel. This beneficial role of in-band relays in the bursty channel is in direct contrast to their role in the non-bursty channel which is not as significant to provide a DoF gain. More importantly, we demonstrate that for certain antenna configurations, an in-band relay can help achieve interference-free performances with increased DoF. We find the benefits particularly substantial with low data traffic, as the DoF gain can grow linearly with the number of antennas at the relay. In this work, we first derive an outer bound from which we obtain a necessary condition for interference-free DoF performances. Then, we develop a novel scheme that exploits information of the bursty traffic states to achieve them.

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arXiv2014

Degrees of Freedom of Uplink-Downlink Multiantenna Cellular Networks

An uplink-downlink two-cell cellular network is studied in which the first base station (BS) with $M_1$ antennas receives independent messages from its $N_1$ serving users, while the second BS with $M_2$ antennas transmits independent messages to its $N_2$ serving users. That is, the first and second cells operate as uplink and downlink, respectively. Each user is assumed to have a single antenna. Under this uplink-downlink setting, the sum degrees of freedom (DoF) is completely characterized as the minimum of $(N_1N_2+\min(M_1,N_1)(N_1-N_2)^++\min(M_2,N_2)(N_2-N_1)^+)/\max(N_1,N_2)$, $M_1+N_2,M_2+N_1$, $\max(M_1,M_2)$, and $\max(N_1,N_2)$, where $a^+$ denotes $\max(0,a)$. The result demonstrates that, for a broad class of network configurations, operating one of the two cells as uplink and the other cell as downlink can strictly improve the sum DoF compared to the conventional uplink or downlink operation, in which both cells operate as either uplink or downlink. The DoF gain from such uplink-downlink operation is further shown to be achievable for heterogeneous cellular networks having hotspots and with delayed channel state information.

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arXiv2014

Opportunistic Downlink Interference Alignment

In this paper, we propose an opportunistic downlink interference alignment (ODIA) for interference-limited cellular downlink, which intelligently combines user scheduling and downlink IA techniques. The proposed ODIA not only efficiently reduces the effect of inter-cell interference from other-cell base stations (BSs) but also eliminates intra-cell interference among spatial streams in the same cell. We show that the minimum number of users required to achieve a target degrees-of-freedom (DoF) can be fundamentally reduced, i.e., the fundamental user scaling law can be improved by using the ODIA, compared with the existing downlink IA schemes. In addition, we adopt a limited feedback strategy in the ODIA framework, and then analyze the required number of feedback bits leading to the same performance as that of the ODIA assuming perfect feedback. We also modify the original ODIA in order to further improve sum-rate, which achieves the optimal multiuser diversity gain, i.e., $\log \log N$, per spatial stream even in the presence of downlink inter-cell interference, where $N$ denotes the number of users in a cell. Simulation results show that the ODIA significantly outperforms existing interference management techniques in terms of sum-rate in realistic cellular environments. Note that the ODIA operates in a distributed and decoupled manner, while requiring no information exchange among BSs and no iterative beamformer optimization between BSs and users, thus leading to an easier implementation.

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arXiv2014

Information Theory of Matrix Completion

Matrix completion is a fundamental problem that comes up in a variety of applications like the Netflix problem, collaborative filtering, computer vision, and crowdsourcing. The goal of the problem is to recover a k-by-n unknown matrix from a subset of its noiseless (or noisy) entries. We define an information-theoretic notion of completion capacity C that quantifies the maximum number of entries that one observation of an entry can resolve. This number provides the minimum number m of entries required for reliable reconstruction: m=kn/C. Translating the problem into a distributed joint source-channel coding problem with encoder restriction, we characterize the completion capacity for a wide class of stochastic models of the unknown matrix and the observation process. Our achievability proof is inspired by that of the Slepian-Wolf theorem. For an arbitrary stochastic matrix, we derive an upper bound on the completion capacity.

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arXiv2014

Linear Degrees of Freedom of the X-Channel with Delayed CSIT

We establish the degrees of freedom of the two-user X-channel with delayed channel knowledge at transmitters (i.e., delayed CSIT), assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear degrees of freedom of this network to be 6/5. The converse builds upon our development of a general lemma that shows that, if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. As a byproduct, we also apply this general lemma to the three-user interference channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its linear degrees of freedom. This is the first bound that captures the impact of delayed CSIT on the degrees of freedom of this network, under the assumption of linear encoding strategies.

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arXiv2013

Degrees of Freedom of the Rank-deficient Interference Channel with Feedback

We investigate the total degrees of freedom (DoF) of the K-user rank-deficient interference channel with feedback. For the two-user case, we characterize the total DoF by developing an achievable scheme and deriving a matching upper bound. For the three-user case, we develop a new achievable scheme which employs interference alignment to efficiently utilize the dimension of the received signal space. In addition, we derive an upper bound for the general K-user case and show the tightness of the bound when the number of antennas at each node is sufficiently large. As a consequence of these results, we show that feedback can increase the DoF when the number of antennas at each node is large enough as compared to the ranks of channel matrices. This finding is in contrast to the full-rank interference channel where feedback provides no DoF gain. The gain comes from using feedback to provide alternative signal paths, thereby effectively increasing the ranks of desired channel matrices.

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arXiv2013

A New Achievable Scheme for Interference Relay Channels

We establish an achievable rate region for discrete memoryless interference relay channels that consist of two source-destination pairs and one or more relays. We develop an achievable scheme combining Han-Kobayashi and noisy network coding schemes. We apply our achievability to two cases. First, we characterize the capacity region of a class of discrete memoryless interference relay channels. This class naturally generalizes the injective deterministic discrete memoryless interference channel by El Gamal and Costa and the deterministic discrete memoryless relay channel with orthogonal receiver components by Kim. Moreover, for the Gaussian interference relay channel with orthogonal receiver components, we show that our scheme achieves a better sum rate than that of noisy network coding.

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arXiv2012

Approximate Feedback Capacity of the Gaussian Multicast Channel

We characterize the capacity region to within log{2(M-1)} bits/s/Hz for the M-transmitter K-receiver Gaussian multicast channel with feedback where each receiver wishes to decode every message from the M transmitters. Extending Cover-Leung's achievable scheme intended for (M,K)=(2,1), we show that this generalized scheme achieves the cutset-based outer bound within log{2(M-1)} bits per transmitter for all channel parameters. In contrast to the capacity in the non-feedback case, the feedback capacity improves upon the naive intersection of the feedback capacities of K individual multiple access channels. We find that feedback provides unbounded multiplicative gain at high signal-to-noise ratios as was shown in the Gaussian interference channel. To complement the results, we establish the exact feedback capacity of the Avestimehr-Diggavi-Tse (ADT) deterministic model, from which we make the observation that feedback can also be beneficial for function computation.

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arXiv2012

Interference Channels with Rate-Limited Feedback

We consider the two-user interference channel with rate-limited feedback. Related prior works focus on the case where feedback links have infinite capacity, while no research has been done for the rate-limited feedback problem. Several new challenges arise due to the capacity limitations of the feedback links, both in deriving inner-bounds and outer-bounds. We study this problem under three different interference models: the El Gamal-Costa deterministic model, the linear deterministic model, and the Gaussian model. For the first two models, we develop an achievable scheme that employs three techniques: Han-Kobayashi message splitting, quantize-and-binning, and decode-and-forward. We also derive new outer-bounds for all three models and we show the optimality of our scheme under the linear deterministic model. In the Gaussian case, we propose a transmission strategy that incorporates lattice codes, inspired by the ideas developed in the first two models. For symmetric channel gains, we prove that the gap between the achievable sum-rate of the proposed scheme and our new outer-bounds is bounded by a constant number of bits, independent of the channel gains.

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arXiv2012

Two-way Interference Channels

We consider two-way interference channels (ICs) where forward and backward channels are ICs but not necessarily the same. We first consider a scenario where there are only two forward messages and feedback is offered through the backward IC for aiding forward-message transmission. For a linear deterministic model of this channel, we develop inner and outer bounds that match for a wide range of channel parameters. We find that the backward IC can be more efficiently used for feedback rather than if it were used for sending its own independent backward messages. As a consequence, we show that feedback can provide a net increase in capacity even if feedback cost is taken into consideration. Moreover we extend this to a more general scenario with two additional independent backward messages, from which we find that interaction can provide an arbitrarily large gain in capacity.

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arXiv2010

Downlink Interference Alignment

We develop an interference alignment (IA) technique for a downlink cellular system. In the uplink, IA schemes need channel-state-information exchange across base-stations of different cells, but our downlink IA technique requires feedback only within a cell. As a result, the proposed scheme can be implemented with a few changes to an existing cellular system where the feedback mechanism (within a cell) is already being considered for supporting multi-user MIMO. Not only is our proposed scheme implementable with little effort, it can in fact provide substantial gain especially when interference from a dominant interferer is significantly stronger than the remaining interference: it is shown that in the two-isolated cell layout, our scheme provides four-fold gain in throughput performance over a standard multi-user MIMO technique. We show through simulations that our technique provides respectable gain under a more realistic scenario: it gives approximately 20% gain for a 19 hexagonal wrap-around-cell layout. Furthermore, we show that our scheme has the potential to provide substantial gain for macro-pico cellular networks where pico-users can be significantly interfered with by the nearby macro-BS.

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