Achievable Tradeoff Research Articles

Robustness of Sparse Recovery via <inline-formula> <tex-math notation="LaTeX">$F$ </tex-math></inline-formula>-Minimization: A Topological Viewpoint

A recent trend in compressed sensing is to consider non-convex optimization techniques for sparse recovery. The important case of $F$-minimization has become of particular interest, for which the exact reconstruction condition (ERC) in the noiseless setting can be precisely characterized by the null space property (NSP). However, little work has been done concerning its robust reconstruction condition (RRC) in the noisy setting. We look at the null space of the measurement matrix as a point on the Grassmann manifold, and then study the relation between the ERC and RRC sets, denoted as $\Omega_J$ and $\Omega_J^r$, respectively. It is shown that $\Omega_J^r$ is the interior of $\Omega_J$, from which a previous result of the equivalence of ERC and RRC for $\ell_p$-minimization follows easily as a special case. Moreover, when $F$ is non-decreasing, it is shown that $\overline{\Omega}_J\setminus\interior(\Omega_J)$ is a set of measure zero and of the first category. As a consequence, the probabilities of ERC and RRC are the same if the measurement matrix $\mathbf{A}$ is randomly generated according to a continuous distribution. Quantitatively, if the null space $\mathcal{N}(\bf A)$ lies in the "$d$-interior" of $\Omega_J$, then RRC will be satisfied with the robustness constant $C=\frac{2+2d}{d\sigma_{\min}(\mathbf{A}^{\top})}$; and conversely if RRC holds with $C=\frac{2-2d}{d\sigma_{\max}(\mathbf{A}^{\top})}$, then $\mathcal{N}(\bf A)$ must lie in $d$-interior of $\Omega_J$. We also present several rules for comparing the performances of different cost functions. Finally, these results are capitalized to derive achievable tradeoffs between the measurement rate and robustness with the aid of Gordon's escape through the mesh theorem or a connection between NSP and the restricted eigenvalue condition.

On the Achievable Performance-Complexity Tradeoffs of Relay-Aided Space Shift Keying

Future cellular networks require transmission technologies and protocols that are energy-efficient, and that can meet the growing demands of mobile data traffic with the best performance versus complexity tradeoff. The recently proposed single-RF space shift keying (SSK-) multiple-input-multiple-output (MIMO) transmission scheme is one of such physical layer technology that satisfies these criteria. In general, SSK requires a large number of antenna elements (with only one of them active) at the transmitter for high data rate transmission. This makes SSK particularly useful for the downlink of cellular systems. In this paper, we exploit the virtual MIMO concept to design SSK transmission schemes for the uplink of cellular networks. The idea is to take advantage of nearby nodes to the mobile terminal as a “virtual spatial-constellation diagram,” where the information can be encoded and transmitted to the final destination. By taking into account the virtual nature of the spatial-constellation diagram, we develop advanced demodulation techniques, perform a comprehensive mathematical analysis, as well as analyze the system complexity and energy consumption. It is also shown that the proposed scheme is capable of outperforming certain state-of-the-art protocols.

Distributed Space–Time Interference Alignment With Moderately Delayed CSIT

This paper proposes an interference alignment method with distributed and delayed channel state information at the transmitter (CSIT) for a class of interference networks. The core idea of the proposed method is to align interference signals over time at the unintended receivers in a distributed manner. With the proposed method, achievable trade-offs between the sum of degrees of freedom (sum-DoF) and feedback delay of CSI are characterized in both the X-channel and three-user interference channel to reveal the impact on how the CSI feedback delay affects the sum-DoF of the interference networks. A major implication of derived results is that distributed and moderately- delayed CSIT is useful to strictly improve the sum-DoF over the case of no CSI at the transmitter in a certain class of interference networks. For a class of X-channels, the results show how to optimally use distributed and moderately-delayed CSIT to yield the same sum-DoF as instantaneous and global CSIT. Further, leveraging the proposed transmission method and the known outer bound results, the sum-capacity of the two-user X-channel with a particular set of channel coefficients is characterized within a constant number of bits.

When Are Dynamic Relaying Strategies Necessary in Half-Duplex Wireless Networks?

In this paper, we study a simple question: when are dynamic relaying strategies essential in optimizing the diversity-multiplexing tradeoff (DMT) in half-duplex wireless relay networks? This is motivated by apparently two contrasting results even for a simple three-node network with a single half-duplex relay. When all channels in the system are assumed to be independent and identically fading, a static schedule where the relay listens half the time and transmits half the time combined with quantize-map-and-forward (QMF) relaying is known to achieve the full-duplex performance. However, when there is no direct link between the source and the destination, a dynamic decode-and-forward (DDF) strategy is needed to achieve the optimal tradeoff. In this case, a static schedule is strictly suboptimal and the optimal tradeoff is significantly worse than the full-duplex performance. In this paper, we study the general case when the direct link is neither as strong as the other links nor fully nonexistent, and identify regimes where dynamic schedules are necessary and those where static schedules are enough. We identify four qualitatively different regimes for the single-relay channel, where the tradeoff between diversity and multiplexing is significantly different. We show that in all these regimes one of the above two strategies is sufficient to achieve the optimal tradeoff by developing a new upper bound on the best achievable tradeoff under channel state information available only at the receivers. A natural next question is whether these two strategies are sufficient to achieve the DMT of more general half-duplex wireless networks with a larger number of relays. We propose a generalization of the two existing schemes through a dynamic QMF (DQMF) strategy, where the relay listens for a fraction of time depending on received channel state information but not long enough to be able to decode. We show that such a DQMF strategy is needed to achieve the optimal DMT in a parallel channel with two relays, outperforming both DDF and static QMF strategies.

Cascade Source Coding With a Side Information Vending Machine

The model of a side information vending machine (VM) accounts for scenarios in which the measurement of side information sequences can be controlled via the selection of cost-constrained actions. In this paper, the three-node cascade source coding problem is studied under the assumption that a side information VM is available at the intermediate and/or end node of the cascade. A single-letter characterization of the achievable tradeoff among the transmission rates, distortions in the reconstructions at the intermediate and end node, and cost for acquiring the side information is derived for a number of relevant special cases. It is shown that a joint design of the description, source, and control signals used to guide the selection of the actions at downstream nodes is generally necessary for an efficient use of the available communication links. In particular, for all the considered models, layered coding strategies prove to be optimal, whereby the base layer fulfills two network objectives: 1) determining the actions of downstream nodes and 2) simultaneously providing a coarse description of the source. Design of the optimal coding strategy is shown via examples to depend on both the network topology and action costs. Examples also illustrate the involved performance tradeoffs across the network.

From Instantly Decodable to Random Linear Network Coded Broadcast

Our primary goal in this paper is to better under- stand and extend the achievable tradeoffs between the through- put and decoding delay performance of network coded wireless broadcast. To this end, we traverse the performance gap between two linear network coding schemes: random linear network cod- ing (RLNC) and instantly decodable network coding (IDNC). Our approach is to appropriately partition a block of partially received data packets into subgenerations and broadcast them separately using RLNC. Through analyzing the factors that af- fect the performance of a generic partitioning scheme, we are led to develop a coding framework in which subgenerations are created from IDNC coding sets in an IDNC solution. This coding framework consists of a series of coding schemes, with classic RLNC and IDNC identified as two extreme schemes. We develop two basic partitioning guidelines, including disjoint partitioning and even partitioning. We design various implementations of this coding framework, such as partitioning algorithms and gener- ation scheduling strategies, to further improve its throughput and decoding delay, to manage feedback frequency and coding complexity, or to achieve in-block performance adaption. Their effectiveness is verified through extensive simulations, and their performance is compared with an existing work in the literature.

Diversity Block Code: A Trade-off for Multiplexing and Diversity Gains

Multiple antennas at both transmitter and receiver have been proposed in the literature to obtain spatial multiplexing or diversity based on the system requirement. Analytical approaches have been found in the literature, suggesting obtainable trade-off between multiplexing and diversity. However, there exists no implementable demonstration to achieve the same. In this study, a generator polynomial for a block code namely diversity block code has been proposed that demonstrates achievable trade-off between multiplexing and diversity. It is found that at low signal to noise ratio, the proposed codes provides the best bit error rate performance in comparison to its counterparts, systems with spatial multiplexing and transmit diversity. Beyond 7dB SNR, the system with the proposed code is being superior to the system with spatial multiplexing.

Alternative relaying for cooperative multiple-access channels in wireless vehicular networks

In this paper, a novel spectrally efficient half-duplex cooperative transmission protocol is proposed for cooperative multiple-access channels in wireless vehicular networks, where multiple sources (vehicles) deliver messages to a common destination (roadside base station or roadside infrastructure) with the help of multiple decode-and-forward relays (roadside stations). The basic idea is to apply superposition coding at each transmitter in order to achieve the full diversity gain, where the linear zero-forcing detection is used at each relay to combat inter-relay interference. Compared to existing uplink cooperative protocols, the proposed scheme can exploit the cooperation involving both the relays and the sources. An achievable diversity-multiplexing trade-off is developed for the proposed transmission protocol. Even with strong inter-relay interference which has been ignored by many existing works, the proposed scheme can still approach the optimal multiple-input single-output upper bound. Numerical results have also been provided to demonstrate the performance of the proposed protocol.

Finite‐SNR diversity‐multiplexing trade‐off of inter‐vehicular cooperative diversity protocols

The finite-signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of cooperative diversity protocols are investigated in vehicular networks based on cascaded Rayleigh fading. Lower bounds of DMT at finite SNR for orthogonal and non-orthogonal protocols are derived. The results showcase the first look into the achievable DMT trade-off of cooperative diversity in volatile vehicular environments. It is shown that the diversity gains are significantly suboptimal at realistic SNRs.

Asymptotic Throughput and Throughput-Delay Scaling in Wireless Networks: The Impact of Error Propagation

This paper analyzes the impact of error propagation on the achievable throughput and throughput-delay tradeoff in wireless networks. It addresses the particular class of multihop routing schemes for parallel unicast that achieve a throughput scaling of Θ(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> ) per node in a network of n nodes. It is shown that in the finite-block-length case, necessitated by finite decoding memory at the nodes, the guaranteed per-node throughput in the network cannot scale better than o (n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-r</sup> ) per node for any r > 0. This bound on the guaranteed per-node throughput is tighter than the O (1/n) bound shown previously. Instead of focusing on the probability of error for each link, which is intractable, an approach of bounding mutual information is employed to show tight results on the achievable throughput and throughput-delay tradeoffs. It is shown that for multihop transmission protocols, error propagation leads to significant changes in the tradeoff between the throughput T(n) and the delay D(n), compared to previous results. The best known scaling behavior is only D(n) = Θ (n (log n) T(n)) under maximum throughput scaling, where the block length required scales as Ω (log n). When decoding memory at nodes is constrained to be O (log log n), the achievable tradeoff worsens to D(n) = Θ (n (log n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> T(n)).

Reliability-Configurable Mixed-Grained Reconfigurable Array Supporting C-Based Design and Its Irradiation Testing

This paper proposes a mixed-grained reconfigurable architecture consisting of fine-grained and coarse-grained fabrics, each of which can be configured for different levels of reliability depending on the reliability requirement of target applications, e.g. mission-critical applications to consumer products. Thanks to the fine-grained fabrics, the architecture can accommodate a state machine, which is indispensable for exploiting C-based behavioral synthesis to trade latency with resource usage through multi-step processing using dynamic reconfiguration. In implementing the architecture, the strategy of dynamic reconfiguration, the assignment of configuration storage and the number of implementable states are key factors that determine the achievable trade-off between used silicon area and latency. We thus split the configuration bits into two classes; state-wise configuration bits and state-invariant configuration bits for minimizing area overhead of configuration bit storage. Through a case study, we experimentally explore the appropriate number of implementable states. A proof-of-concept VLSI chip was fabricated in 65 nm process. Measurement results show that applications on the chip can be working in a harsh radiation environment. Irradiation tests also show the correlation between the number of sensitive bits and the mean time to failure. Furthermore, the temporal error rate of an example application due to soft errors in the datapath was measured and demonstrated for reliability-aware mapping. key words: reconfigurable architecture, soft error, radiation test, behavioral synthesis, state machine

On the Performance of Diagonal Lattice Space-Time Codes

There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria . In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding.

Achievable complexity-performance tradeoffs in lossy compression

We present several results related to the complexity-performance tradeoff in lossy compression. The first result shows that for a memoryless source with rate-distortion function R(D) and a bounded distortion measure, the rate-distortion point (R(D) + ?, D + ?) can be achieved with constant decompression time per (separable) symbol and compression time per symbol proportional to $$\left( {{{\lambda _1 } \mathord{\left/ {\vphantom {{\lambda _1 } \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }} \right)^{{{\lambda _2 } \mathord{\left/ {\vphantom {{\lambda _2 } {\gamma ^2 }}} \right. \kern-\nulldelimiterspace} {\gamma ^2 }}}$$ , where ? 1 and ? 2 are source dependent constants. The second result establishes that the same point can be achieved with constant decompression time and compression time per symbol proportional to $$\left( {{{\rho _1 } \mathord{\left/ {\vphantom {{\rho _1 } \gamma }} \right. \kern-\nulldelimiterspace} \gamma }} \right)^{{{\rho _2 } \mathord{\left/ {\vphantom {{\rho _2 } {\varepsilon ^2 }}} \right. \kern-\nulldelimiterspace} {\varepsilon ^2 }}}$$ . These results imply, for any function g(n) that increases without bound arbitrarily slowly, the existence of a sequence of lossy compression schemes of blocklength n with O(ng(n)) compression complexity and O(n) decompression complexity that achieve the point (R(D), D) asymptotically with increasing blocklength. We also establish that if the reproduction alphabet is finite, then for any given R there exists a universal lossy compression scheme with O(ng(n)) compression complexity and O(n) decompression complexity that achieves the point (R, D(R)) asymptotically for any stationary ergodic source with distortion-rate function D(·).

Buffer-Aware Network Coding for Wireless Networks

Network coding, which can combine various traffic flows or packets via algebraic operations, has the potential of achieving substantial throughput and power efficiency gains in wireless networks. As such, it is considered as a powerful solution to meet the stringent demands and requirements of next-generation wireless systems. However, because of the random and asynchronous packet arrivals, network coding may result in severe delay and packet loss because packets need to wait to be network-coded with each others. To overcome this and guarantee quality of service (QoS), we present a novel cross-layer approach, which we shall refer to as Buffer-Aware Network Coding, or BANC, which allows transmission of some packets without network coding to reduce the packet delay. We shall derive the average delay and power consumption of BANC by presenting a random mapping description of BANC and Markov models of buffer states. A cross-layer optimization problem that minimizes the average delay under a given power constraint is then proposed and analyzed. Its solution will not only demonstrate the fundamental performance limits of BANC in terms of the achievable delay region and delay-power tradeoff, but also obtains the delay-optimal BANC schemes. Simulation results will show that the proposed approach can strike the optimal tradeoff between power efficiency and QoS.

Pareto‐Set Analysis: Biobjective Clustering in Decision and Objective Spaces

ABSTRACTMultiobjective problems usually contain conflicting objectives. Therefore, there is no single best solution but a set of solutions that represent different tradeoffs between these objectives. Knowledge of this front can help in understanding the optimization problem better, as promising designs can be identified, and it can be seen what the achievable tradeoffs between the objective values are. Although for real‐world problems, this interpretation of the front is usually not straightforward.This paper proposes a method to help the decision maker by clustering a given set of tradeoff solutions. It does so by extending the standard approach of clustering the solutions in objective space, such that it finds clusters that are compact and well separated both in decision space and in objective space. It is not the goal of the method to provide the decision maker with a single preferred solution. Instead, it helps the decision maker by structuring the tradeoff solutions such that he or she can learn about the problem. More precisely, a good clustering of the tradeoff solutions both in decision space and in objective space elicits information from the front about what design types lead to what regions in objective space. The novelty of the presented approach over existing work is its general nature, as it does not require the identification of distinct design variables or feature vectors. Instead, the proposed method only requires that a distance measure between a given pair of solutions can be calculated both in decision space and in objective space.As good clusters in decision space do not necessarily correspond to good clusters in objective space, we formulate this clustering problem as a biobjective optimization problem and propose PAN, a multiobjective evolutionary algorithm, to generate promising partitionings. Tests on artificial datasets are used to identify a suitable representation and a suitable partitioning goodness measure for PAN. Results from applying PAN to a knapsack problem and a bridge construction problem show that PAN is able to find multiple tradeoffs between good clustering in decision space and in objective space. Copyright © 2012 John Wiley &amp; Sons, Ltd.

On the Optimum Diversity–Multiplexing Tradeoff of the Two-User Gaussian Interference Channel With Rayleigh Fading

In this paper, the optimum tradeoff between diversity and multiplexing gains in a two-user quasi-static Rayleigh fading interference channel (IC) is studied. The diversity and multiplexing gains are two basic performance measures in wireless networks which characterize the transmission reliability and the data rate, respectively. It would be of interest to investigate the optimal tradeoff between these two measures. First, we develop a coding scheme for the two-user quasi-static Rayleigh fading Gaussian IC with interference level α := log INR/log SNR ≥ 1. Then, for this coding scheme the achievable diversity-multiplexing tradeoff (DMT) is characterized. Our achievable DMT coincides with its outer bound. In the low and high rate regions (to be defined later), the proposed coding scheme is a one-level Gaussian code, independent of the channel state information (CSI). In the middle rate region (to be defined later), the proposed coding scheme, depending on the partial CSI, can be a one-level or a two-level Gaussian code. We show that the relevant partial CSI can be represented by only one bit determined by the absolute value of the channel gain. In the middle rate region, we assume that the single-bit partial CSI for all the four channel gains of the Gaussian IC are available at both transmitters.

Information Trade-Offs for Optical Quantum Communication

Recent work has precisely characterized the achievable trade-offs between three key information processing tasks-classical communication (generation or consumption), quantum communication (generation or consumption), and shared entanglement (distribution or consumption), measured in bits, qubits, and ebits per channel use, respectively. Slices and corner points of this three-dimensional region reduce to well-known protocols for quantum channels. A trade-off coding technique can attain any point in the region and can outperform time sharing between the best-known protocols for accomplishing each information processing task by itself. Previously, the benefits of trade-off coding that had been found were too small to be of practical value (viz., for the dephasing and the universal cloning machine channels). In this Letter, we demonstrate that the associated performance gains are in fact remarkably high for several physically relevant bosonic channels that model free-space or fiber-optic links, thermal-noise channels, and amplifiers. We show that significant performance gains from trade-off coding also apply when trading photon-number resources between transmitting public and private classical information simultaneously over secret-key-assisted bosonic channels.

Distortion Exponents of Two-Way Relay Networks

In this paper, we study the transmission of Gaussian signals in a three-node two-way relay network, where two users communicate in both directions at possibly different rates, with the help of one relay. All nodes are half-duplex and equipped with single antenna. The relay employs the amplify-and-forward (AF) or decode-and-forward (DF) based cooperation protocols. We analyze the distortion exponent that characterizes the high signal-to-noise ratio (SNR) behavior of the end-to-end distortion of the reconstructed signal at each user node. The different rates of the two users necessitate the study of a new concept - the achievable distortion exponent region of the system. We first derive an outer bound on the distortion exponent region of two-way relay communications, which is tight at large bandwidth ratios. We then obtain the optimized distortion exponent pairs of simple four-phase relay strategies as well as two-phase and three-phase protocols. The results illustrate the effect of the bandwidth ratio and cooperation strategies on the optimized distortion exponents. Another contribution of the paper is that we also derive the achievable diversity-multiplexing tradeoffs (DMTs) of different two-way relay protocols.

Power Control and Channel Training for MIMO Channels: A DMT Perspective

The achievable diversity and multiplexing tradeoff (DMT) in MIMO fading channels with channel training is analyzed in this paper. We first consider a typical training scenario, where the transmitter transmits training symbols followed by data symbols, and the receiver performs channel estimation using the training symbols and then uses the imperfect channel estimates to decode the data symbols. From the DMT perspective, our results show that as long as the training power is equal to the data power, the obtained DMT result based on imperfect channel state information at receiver (CSIR) is the same as the original DMT result with perfect CSIR given in Zheng and Tse's seminal work . We extend the analysis to two-way training scenarios, with single and multiple training rounds. Our results show that two-way training together with power control can substantially improve the achievable diversity gain. Specifically, the achievable DMT with multiple training rounds can be described as a single straight line; while in the case of single training round, the achievable DMT is much lower and can be described as a single straight line or a collection of line segments, depending on the underlying training strategy and channel qualities.

Source Coding With a Side Information “Vending Machine”

We study source coding in the presence of side information, when the system can take actions that affect the availability, quality, or nature of the side information. We begin by extending the Wyner-Ziv problem of source coding with decoder side information to the case where the decoder is allowed to choose actions affecting the side information. We then consider the setting where actions are taken by the encoder, based on its observation of the source. Actions may have costs that are commensurate with the quality of the side information they yield, and an overall per-symbol cost constraint may be imposed. We characterize the achievable tradeoffs between rate, distortion, and cost in some of these problem settings. Among our findings is the fact that even in the absence of a cost constraint, greedily choosing the action associated with the “best” side information is, in general, suboptimal. A few examples are worked out.