arXiv subjects

Daniela Tuninetti

Publications and source records attributed to Daniela Tuninetti.

At least 91 records · Page 5Linked to original sources

arXiv2013

Message Error Analysis of Loopy Belief Propagation for the Sum-Product Algorithm

Belief propagation is known to perform extremely well in many practical statistical inference and learning problems using graphical models, even in the presence of multiple loops. The iterative use of belief propagation algorithm on loopy graphs is referred to as Loopy Belief Propagation (LBP). Various sufficient conditions for convergence of LBP have been presented; however, general necessary conditions for its convergence to a unique fixed point remain unknown. Because the approximation of beliefs to true marginal probabilities has been shown to relate to the convergence of LBP, several methods have been explored whose aim is to obtain distance bounds on beliefs when LBP fails to converge. In this paper, we derive uniform and non-uniform error bounds on messages, which are tighter than existing ones in literature, and use these bounds to derive sufficient conditions for the convergence of LBP in terms of the sum-product algorithm. We subsequently use these bounds to study the dynamic behavior of the sum-product algorithm, and analyze the relation between convergence of LBP and sparsity and walk-summability of graphical models. We finally use the bounds derived to investigate the accuracy of LBP, as well as the scheduling priority in asynchronous LBP.

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arXiv2013

Approximate Sum-Capacity of K-user Cognitive Interference Channels with Cumulative Message Sharing

This paper considers the K user cognitive interference channel with one primary and K-1 secondary/cognitive transmitters with a cumulative message sharing structure, i.e cognitive transmitter $i\in [2:K]$ knows non-causally all messages of the users with index less than i. We propose a computable outer bound valid for any memoryless channel. We first evaluate the sum-rate outer bound for the high- SNR linear deterministic approximation of the Gaussian noise channel. This is shown to be capacity for the 3-user channel with arbitrary channel gains and the sum-capacity for the symmetric K-user channel. Interestingly. for the K user channel having only the K th cognitive know all the other messages is sufficient to achieve capacity i.e cognition at transmitter 2 to K-1 is not needed. Next the sum capacity of the symmetric Gaussian noise channel is characterized to within a constant additive and multiplicative gap. The proposed achievable scheme for the additive gap is based on Dirty paper coding and can be thought of as a MIMO-broadcast scheme where only one encoding order is possible due to the message sharing structure. As opposed to other multiuser interference channel models, a single scheme suffices for both the weak and strong interference regimes. With this scheme the generalized degrees of freedom (gDOF) is shown to be a function of K, in contrast to the non cognitive case and the broadcast channel case. Interestingly, it is show that as the number of users grows to infinity the gDoF of the K-user cognitive interference channel with cumulative message sharing tends to the gDoF of a broadcast channel with a K-antenna transmitter and K single-antenna receivers. The analytical additive additive and multiplicative gaps are a function of the number of users. Numerical evaluations of inner and outer bounds show that the actual gap is less than the analytical one.

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arXiv2013

On Gaussian Half-Duplex Relay Networks

This paper considers Gaussian relay networks where a source transmits a message to a sink terminal with the help of one or more relay nodes. The relays work in half-duplex mode, in the sense that they can not transmit and receive at the same time. For the case of one relay, the generalized Degrees-of-Freedom is characterized first and then it is shown that capacity can be achieved to within a constant gap regardless of the actual value of the channel parameters. Different achievable schemes are presented with either deterministic or random switch for the relay node. It is shown that random switch in general achieves higher rates than deterministic switch. For the case of K relays, it is shown that the generalized Degrees-of-Freedom can be obtained by solving a linear program and that capacity can be achieved to within a constant gap of K/2log(4K). This gap may be further decreased by considering more structured networks such as, for example, the diamond network.

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arXiv2012

The Capacity of the Gaussian Cooperative Two-user Multiple Access Channel to within a Constant Gap

The capacity region of the cooperative two-user Multiple Access Channel (MAC) in Gaussian noise is determined to within a constant gap for both the Full-Duplex (FD) and Half-Duplex (HD) case. The main contributions are: (a) for both FD and HD: unilateral cooperation suffices to achieve capacity to within a constant gap where only the user with the strongest link to the destination needs to engage in cooperation, (b) for both FD and HD: backward joint decoding is not necessary to achieve capacity to within a constant gap, and (c) for HD: time sharing between the case where the two users do not cooperate and the case where the user with the strongest link to the destination acts as pure relay for the other user suffices to achieve capacity to within a constant gap. These findings show that simple achievable strategies are approximately optimal for all channel parameters with interesting implications for practical cooperative schemes.

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arXiv2012

Achieving Net Feedback Gain in the Butterfly Network with a Full-Duplex Bidirectional Relay

A symmetric butterfly network (BFN) with a full-duplex relay operating in a bi-directional fashion for feedback is considered. This network is relevant for a variety of wireless networks, including cellular systems dealing with cell-edge users. Upper bounds on the capacity region of the general memoryless BFN with feedback are derived based on cut-set and cooperation arguments and then specialized to the linear deterministic BFN with really-source feedback. It is shown that the upper bounds are achievable using combinations of the compute-forward strategy and the classical decode-and-forward strategy, thus fully characterizing the capacity region. It is shown that net rate gains are possible in certain parameter regimes.

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arXiv2012

An Outer Bound for the Memoryless Two-user Interference Channel with General Cooperation

The interference channel models a wireless network where several source-destination pairs compete for the same resources. When nodes transmit simultaneously the destinations experience interference. This paper considers a 4-node network, where two nodes are sources and the other two are destinations. All nodes are full-duplex and cooperate to mitigate interference. A sum-rate outer bound is derived, which is shown to unify a number of previously derived outer bounds for special cases of cooperation. The approach is shown to extend to cooperative interference networks with more than two source-destination pairs and for any partial sum-rate. How the derived bound relates to similar bounds for channel models including cognitive nodes, i.e., nodes that have non-causal knowledge of the messages of some other node, is also discussed. Finally, the bound is evaluated for the Gaussian noise channel and used to compare different modes of cooperation.

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arXiv2011

On the Capacity of the Interference Channel with a Cognitive Relay

The InterFerence Channel with a Cognitive Relay (IFC-CR) consists of the classical interference channel with two independent source-destination pairs whose communication is aided by an additional node, referred to as the cognitive relay, that has a priori knowledge of both sources' messages. This a priori message knowledge is termed cognition and idealizes the relay learning the messages of the two sources from their transmissions over a wireless channel. This paper presents new inner and outer bounds for the capacity region of the general memoryless IFC-CR that are shown to be tight for a certain class of channels. The new outer bound follows from arguments originally devised for broadcast channels among which Sato's observation that the capacity region of channels with non-cooperative receivers only depends on the channel output conditional marginal distributions. The new inner bound is shown to include all previously proposed coding schemes and it is thus the largest known achievable rate region to date. The new inner and outer bounds coincide for a subset of channel satisfying a strong interference condition. For these channels there is no loss in optimality if both destinations decode both messages. This result parallels analogous results for the classical IFC and for the cognitive IFC and is the first known capacity result for the general IFC-CR. Numerical evaluations of the proposed inner and outer bounds are presented for the Gaussian noise case.

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arXiv2011

On the Benefits of Partial Channel State Information for Repetition Protocols in Block Fading Channels

This paper studies the throughput performance of HARQ (hybrid automatic repeat request) protocols over block fading Gaussian channels. It proposes new protocols that use the available feedback bit(s) not only to request a retransmission, but also to inform the transmitter about the instantaneous channel quality. An explicit protocol construction is given for any number of retransmissions and any number of feedback bits. The novel protocol is shown to simultaneously realize the gains of HARQ and of power control with partial CSI (channel state information). Remarkable throughput improvements are shown, especially at low and moderate SNR (signal to noise ratio), with respect to protocols that use the feedback bits for retransmission request only. In particular, for the case of a single retransmission and a single feedback bit, it is shown that the repetition is not needed at low $\snr$ where the throughput improvement is due to power control only. On the other hand, at high SNR, the repetition is useful and the performance gain comes form a combination of power control and ability of make up for deep fades.

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arXiv2011

Capacity to within 3 bits for a class of Gaussian Interference Channels with a Cognitive Relay

The InterFerence Channel with a Cognitive Relay (IFC-CR) consists of a classical two-user interference channel in which the two independent messages are also non-causally known at a cognitive relay node. In this work a special class of IFC-CRs in which the sources do not create interference at the non-intended destinations is analyzed. This special model results in a channel with two non-interfering point-to-point channels whose transmission is aided by an in-band cognitive relay, which is thus referred to as the Parallel Channel with a Cognitive Relay (PC-CR). We determine the capacity of the PC-CR channel to within 3 bits/s/Hz for all channel parameters. In particular, we present several new outer bounds which we achieve to within a constant gap by proper selection of Gaussian input distributions in a simple rate-splitting and superposition coding-based inner bound. The inner and outer bounds are numerically evaluated to show that the actual gap can be far less than 3 bits/s/Hz.

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arXiv2011

A New Capacity Result for the Z-Gaussian Cognitive Interference Channel

This work proposes a novel outer bound for the Gaussian cognitive interference channel in strong interference at the primary receiver based on the capacity of a multi-antenna broadcast channel with degraded message set. It then shows that for the Z-channel, i.e., when the secondary receiver experiences no interference and the primary receiver experiences strong interference, the proposed outer bound not only is the tightest among known bounds but is actually achievable for sufficiently strong interference. The latter is a novel capacity result that from numerical evaluations appears to be generalizable to a larger (i.e., non-Z) class of Gaussian channels.

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arXiv2011

The Capacity of the Interference Channel with a Cognitive Relay in Very Strong Interference

The interference channel with a cognitive relay consists of a classical interference channel with two sourcedestination pairs and with an additional cognitive relay that has a priori knowledge of the sources' messages and aids in the sources' transmission. We derive a new outer bound for this channel using an argument originally devised for the "more capable" broadcast channel, and show the achievability of the proposed outer bound in the "very strong interference" regime, a class of channels where there is no loss in optimality if both destinations decode both messages. This result is analogous to the "very strong interference" capacity result for the classical interference channel and for the cognitive interference channel, and is the first capacity known capacity result for the general interference channel with a cognitive relay.

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arXiv2011

K-user Interference Channels: General Outer Bound and Sum-capacity for Certain Gaussian Channels

This paper derives an outer bound on the capacity region of a general memoryless interference channel with an arbitrary number of users. The derivation follows from a generalization of the techniques developed by Kramer and by Etkin et al for the Gaussian two-user channel. The derived bound is the first known outer bound valid for any memoryless channel. In Gaussian noise, classes of channels for which the proposed bound gives the sum-rate capacity are identified, including degraded channels and a class of Z-channels.

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arXiv2011

A New Sum-Rate Outer Bound for Interference Channels with Three Source-Destination Pairs

This paper derives a novel sum-rate outer bound for the general memoryless interference channel with three users. The derivation is a generalization of the techniques developed by Kramer and by Etkin et al for the Gaussian two-user channel. For the three-user Gaussian channel the proposed sum-rate outer bound outperforms known bounds for certain channel parameters.

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arXiv2010

Inner and Outer Bounds for the Gaussian Cognitive Interference Channel and New Capacity Results

The capacity of the Gaussian cognitive interference channel, a variation of the classical two-user interference channel where one of the transmitters (referred to as cognitive) has knowledge of both messages, is known in several parameter regimes but remains unknown in general. In this paper we provide a comparative overview of this channel model as we proceed through our contributions: we present a new outer bound based on the idea of a broadcast channel with degraded message sets, and another series of outer bounds obtained by transforming the cognitive channel into channels with known capacity. We specialize the largest known inner bound derived for the discrete memoryless channel to the Gaussian noise channel and present several simplified schemes evaluated for Gaussian inputs in closed form which we use to prove a number of results. These include a new set of capacity results for the a) "primary decodes cognitive" regime, a subset of the "strong interference" regime that is not included in the "very strong interference" regime for which capacity was known, and for the b) "S-channel" in which the primary transmitter does not interfere with the cognitive receiver. Next, for a general Gaussian cognitive interference channel, we determine the capacity to within one bit/s/Hz and to within a factor two regardless of channel parameters, thus establishing rate performance guarantees at high and low SNR, respectively. We also show how different simplified transmission schemes achieve a constant gap between inner and outer bound for specific channels. Finally, we numerically evaluate and compare the various simplified achievable rate regions and outer bounds in parameter regimes where capacity is unknown, leading to further insight on the capacity region of the Gaussian cognitive interference channel.

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arXiv2010

On Repetition Protocols and Power Control for Multiple Access Block-Fading Channels

In this paper we study the long-term throughput performance of repetition protocols coupled with power control for multiple access block-fading channels. We propose to use the feedback bits to inform the transmitter about the decoding status and the instantaneous channel quality. We determine the throughput of simple and practically inspired protocols; we show remarkable throughput improvements, especially at low and moderate SNR, when compared to protocols where the feedback bits are used for acknowledgment only or for power control only; we show that the throughput is very close to the ultimate ergodic multi-user water-filling capacity for small number of feedback bits and/or retransmissions. For symmetric Rayleigh fading channels, numerical results show that the throughput improvement is mainly due to the ability to perform a power control, rather than to retransmit.

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arXiv2010

The Capacity of the Semi-Deterministic Cognitive Interference Channel and its Application to Constant Gap Results for the Gaussian Channel

The cognitive interference channel (C-IFC) consists of a classical two-user interference channel in which the message of one user (the "primary" user) is non-causally available at the transmitter of the other user (the "cognitive" user). We obtain the capacity of the semi-deterministic C-IFC: a discrete memoryless C-IFC in which the cognitive receiver output is a noise-less deterministic function of the channel inputs. We then use the insights obtained from the capacity-achieving scheme for the semi-deterministic model to derive new, unified and tighter constant gap results for the complex-valued Gaussian C-IFC. We prove: (1) a constant additive gap (difference between inner and outer bounds) of half a bit/sec/Hz per real dimension, of relevance at high SNRs, and (b) a constant multiplicative gap (ratio between outer and inner bounds) of a factor two, of relevance at low SNRs

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arXiv2010

New Results on the Capacity of the Gaussian Cognitive Interference Channel

The capacity of the two-user Gaussian cognitive interference channel, a variation of the classical interference channel where one of the transmitters has knowledge of both messages, is known in several parameter regimes but remains unknown in general. In this paper, we consider the following achievable scheme: the cognitive transmitter pre-codes its message against the interference created at its intended receiver by the primary user, and the cognitive receiver only decodes its intended message, similar to the optimal scheme for "weak interference"; the primary decoder decodes both messages, similar to the optimal scheme for "very strong interference". Although the cognitive message is pre-coded against the primary message, by decoding it, the primary receiver obtains information about its own message, thereby improving its rate. We show: (1) that this proposed scheme achieves capacity in what we term the "primary decodes cognitive" regime, i.e., a subset of the "strong interference" regime that is not included in the "very strong interference" regime for which capacity was known; (2) that this scheme is within one bit/s/Hz, or a factor two, of capacity for a much larger set of parameters, thus improving the best known constant gap result; (3) we provide insights into the trade-off between interference pre-coding at the cognitive encoder and interference decoding at the primary receiver based on the analysis of the approximate capacity results.

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arXiv2010

Interference Channel with Generalized Feedback (a.k.a. with source cooperation). Part I: Achievable Region

An Interference Channel with Generalized Feedback (IFC-GF) is a model for a wireless network where several source-destination pairs compete for the same channel resources, and where the sources have the ability to sense the current channel activity. The signal overheard from the channel provides information about the activity of the other users, and thus furnishes the basis for cooperation. In this two-part paper we study achievable strategies and outer bounds for a general IFC-GF with two source-destination pairs. We then evaluate the proposed regions for the Gaussian channel. Part I: achievable region. We propose that the generalized feedback is used to gain knowledge about the message sent by other user and then exploited in two ways: (a) to {\em relay} the messages that can be decoded at both destinations--thus realizing the gains of beam-forming of a distributed multi-antenna system--and (b) to {\em hide} the messages that can not be decoded at the non-intended destination--thus leveraging the interference "pre-cancellation" property of dirty-paper-type coding. We show that our achievable region generalizes several known achievable regions for IFC-GF and that it reduces to known achievable regions for some of the channels subsumed by the IFC-GF model.

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