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Noise radars have the same mathematical description as a type of quantum radar known as quantum two-mode squeezing radar. Although their physical implementations are very different, this mathematical similarity allows us to analyze them collectively. We may consider the two types of radars as forming a single class of radars, called noise-type radars. The target detection performance of noise-type radars depends on two parameters: the number of integrated samples and a correlation coefficient. In this paper, we show that when the number of integrated samples is large and the correlation coefficient is low, the detection performance becomes a function of a single parameter: the number of integrated samples multiplied by the square of the correlation coefficient. We then explore the detection performance of noise-type radars in terms of this emergent parameter; in particular, we determine the probability of detection as a function of this parameter., Comment: 7 pages, 7 figures, 2 tables

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the received signal, the amplitude of the internal signal used for matched filtering, the correlation between the two signals, and the relative phase between them. In this paper, we derive estimators for these four parameters using two techniques. The first is based on minimizing the Frobenius norm between the structured covariance matrix and the sample covariance matrix; the second is maximum likelihood parameter estimation. The two techniques yield the same estimators. We then give probability density functions (PDFs) for all four estimators. Because some of these PDFs are quite complicated, we also provide approximate PDFs. Finally, we apply our results to the problem of target detection and derive expressions for the receiver operating characteristic curves of two different noise radar detectors., Comment: 13 pages, 11 figures

We derive a detector that optimizes the target detection performance of any single-input single-output noise radar satisfying the following properties: it transmits Gaussian noise, it retains an internal reference signal for matched filtering, all external noise is additive white Gaussian noise, and all signals are measured using heterodyne receivers. This class of radars, which we call noise-type radars, includes not only many types of standard noise radars, but also a type of quantum radar known as quantum two-mode squeezing radar. The detector, which we derive using the Neyman-Pearson lemma, is not practical because it requires foreknowledge of a target-dependent correlation coefficient that cannot be known beforehand. (It is, however, a natural standard of comparison for other detectors.) This motivates us to study the family of Neyman-Pearson-based detectors that result when the correlation coefficient is treated as a parameter. We derive the probability distribution of the Neyman-Pearson-based detectors when there is a mismatch between the pre-chosen parameter value and the true correlation coefficient. We then use this result to generate receiver operating characteristic curves. Finally, we apply our results to the case where the correlation coefficient is small. It turns out that the resulting detector is not only a good one, but that it has appeared previously in the quantum radar literature., Comment: 8 pages, 10 figures

We derive a detector function for quantum two-mode squeezing (QTMS) radars and noise radars that is based on the use of a likelihood ratio (LR) test for distinguishing between the presence and absence of a target. In addition to an explicit expression for the LR detector, we derive a detector function which approximates the LR detector in the limit where the target is small, far away, or otherwise difficult to detect. When the number of integrated samples is large, we derive a theoretical expression for the receiver operating characteristic (ROC) curve of the radar when the LR detector is used. When the number of samples is small, we use simulations to understand the ROC curve behavior of the detector. One interesting finding is there exists a parameter regime in which a previously-studied detector outperforms the LR detector, contrary to the intuition that LR tests are optimal. This is because neither the Neyman-Pearson lemma, nor the Karlin-Rubin theorem which generalizes the lemma, hold in this particular problem. However, the LR detector remains a good choice for target detection., Comment: 7 pages, 8 figures

Noise radars can be understood in terms of a correlation coefficient which characterizes their detection performance. Although most results in the literature are stated in terms of the signal-to-noise ratio (SNR), we show that it is possible to carry out performance prediction in terms of the correlation coefficient. To this end, we derive the range dependence of the correlation coefficient. We then combine our result with a previously-derived expression for the receiver operating characteristic (ROC) curve of a coherent noise radar, showing that we can obtain ROC curves for varying ranges. A comparison with corresponding results for a conventional radar employing coherent integration shows that our results are sensible. The aim of our work is to show that the correlation coefficient is a viable adjunct to SNR in understanding radar performance., Comment: 5 pages, 3 figures; accepted for publication in IEEE Access

We consider a multi-hypothesis testing problem involving a K-armed bandit. Each arm's signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker incurs a delay cost for delay until a decision and a switching cost whenever he switches from one arm to another. His goal is to minimise the overall cost until a decision is reached on the true hypothesis. Of interest are policies that satisfy a given constraint on the probability of false detection. This is a sequential decision making problem where the decision maker gets only a limited view of the true state of nature at each stage, but can control his view by choosing the arm to observe at each stage. An information-theoretic lower bound on the total cost (expected time for a reliable decision plus total switching cost) is first identified, and a variation on a sequential policy based on the generalised likelihood ratio statistic is then studied. Due to the vector exponential family assumption, the signal processing at each stage is simple; the associated conjugate prior distribution on the unknown model parameters enables easy updates of the posterior distribution. The proposed policy, with a suitable threshold for stopping, is shown to satisfy the given constraint on the probability of false detection. Under a continuous selection assumption, the policy is also shown to be asymptotically optimal in terms of the total cost among all policies that satisfy the constraint on the probability of false detection., Comment: arXiv admin note: text overlap with arXiv:1712.03682

The detection of objects in the presence of significant background noise is a problem of fundamental interest in sensing. In this work, we theoretically analyze a prototype target detection protocol, the quantum temporal correlation (QTC) detection protocol, which is implemented in this work utilizing spontaneous parametric down-converted photon-pair sources. The QTC detection protocol only requires time-resolved photon-counting detection, which is phase-insensitive and therefore suitable for optical target detection. As a comparison to the QTC detection protocol, we also consider a classical phase-insensitive target detection protocol based on intensity detection that is practical in the optical regime. We formulated the target detection problem as a total probe photon transmission estimation problem and obtain an analytical expression of the receiver operating characteristic (ROC) curves. We carry out experiments using a semiconductor waveguide source, which we developed and previously reported. The experimental results agree very well with the theoretical prediction. In particular, we find that in a high-level environment noise and loss, the QTC detection protocol can achieve performance comparable to that of the classical protocol (that is practical in the optical regime) but with \(\simeq 57\) times lower detection time in terms of ROC curve metric. The performance of the QTC detection protocol experiment setup could be further improved with a higher transmission of the reference photon and better detector time uncertainty. Furthermore, the probe photons in the QTC detection protocol are completely indistinguishable from the background noise and therefore useful for covert ranging applications. Finally, our technological platform is highly scalable as well as tunable and thus amenable to large scale integration, which is necessary for practical applications.

In order to enhance LIDAR performance metrics such as target detection sensitivity, noise resilience and ranging accuracy, we exploit the strong temporal correlation within the photon pairs generated in continuous-wave pumped semiconductor waveguides. The enhancement attained through the use of such non-classical sources is measured and compared to a corresponding target detection scheme based on simple photon-counting detection. The performances of both schemes are quantified by the estimation uncertainty and Fisher information of the probe photon transmission, which is a widely adopted sensing figure of merit. The target detection experiments are conducted with high probe channel loss (\(\simeq 1-5\times10^{-5}\)) and formidable environment noise up to 36 dB stronger than the detected probe power of \(1.64\times 10^{-5}\) pW. The experimental result shows significant advantages offered by the enhanced scheme with up to 26.3 dB higher performance in terms of estimation uncertainty, which is equivalent to a reduction of target detection time by a factor of 430 or 146 (21.6 dB) times more resilience to noise. We also experimentally demonstrated ranging with these non-classical photon pairs generated with continuous-wave pump in the presence of strong noise and loss, achieving \(\approx\)5 cm distance resolution that is limited by the temporal resolution of the detectors.

Quantum two-mode squeezing (QTMS) radars and noise radars detect targets by correlating the received signal with an internally stored recording. A covariance matrix can be calculated between the two which, in theory, is a function of a single correlation coefficient. This coefficient can be used to decide whether a target is present or absent. We can estimate the correlation coefficient by minimizing the Frobenius norm between the sample covariance matrix and the theoretically expected form of the matrix. Using simulated data, we show that the estimates follow a Rice distribution whose parameters are simple functions of the underlying, "true" correlation coefficient as well as the number of integrated samples. We obtain an explicit expression for the receiver operating characteristic curve that results when the correlation coefficient is used for target detection. This is an important first step toward performance prediction for QTMS radars., Comment: 7 pages, 5 figures; submitted to IEEE Sensors Journal

The problem of multi-hypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal is to design a policy to find the true hypothesis with minimum expected delay while ensuring that the probability of error is below a given constraint. The decision-maker can control the delay by intelligently choosing the control for observation collection in each time slot. We derive a policy that satisfies the given constraint on the error probability. We also show that the policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay.

We have built and evaluated a prototype quantum radar, which we call a quantum two-mode squeezing radar (QTMS radar), in the laboratory. It operates solely at microwave frequencies; there is no downconversion from optical frequencies. Because the signal generation process relies on quantum mechanical principles, the system is considered to contain a quantum-enhanced radar transmitter. This transmitter generates a pair of entangled microwave signals and transmits one of them through free space, where the signal is measured using a simple and rudimentary receiver. At the heart of the transmitter is a device called a Josephson parametric amplifier (JPA), which generates a pair of entangled signals called two-mode squeezed vacuum (TMSV) at 6.1445 GHz and 7.5376 GHz. These are then sent through a chain of amplifiers. The 7.5376 GHz beam passes through 0.5 m of free space; the 6.1445 GHz signal is measured directly after amplification. The two measurement results are correlated in order to distinguish signal from noise. We compare our QTMS radar to a classical radar setup using conventional components, which we call a two-mode noise radar (TMN radar), and find that there is a significant gain when both systems broadcast signals at -82 dBm. This is shown via a comparison of receiver operator characteristic (ROC) curves. In particular, we find that the quantum radar requires 8 times fewer integrated samples compared to its classical counterpart to achieve the same performance., Comment: 17 pages, 17 figures; submitted to IEEE Transactions on Aerospace and Electronic Systems

We consider the change detection problem where the pre-change observation vectors are purely noise and the post-change observation vectors are noise-corrupted compressive measurements of sparse signals with a common support, measured using a sensing matrix. In general, post-change distribution of the observations depends on parameters such as the support and variances of the sparse signal. When these parameters are unknown, we propose two approaches. In the first approach, we approximate the post-change pdf based on the known parameters such as mutual coherence of the sensing matrix and bounds on the signal variances. In the second approach, we parameterize the post-change pdf with an unknown parameter and try to adaptively estimate this parameter using a stochastic gradient descent method. In both these approaches, we employ CUSUM algorithm with various decision statistics such as the energy of the observations, correlation values with columns of the sensing matrix and the maximum value of such correlations. We study the performance of these approaches and offer insights on the relevance of different decision statistics in different SNR regimes. We also address the problem of designing sensing matrices with small coherence by using designs from quantum information theory. One such design, called SIC POVM, also has an additional structure which allows exact computation of the post-change pdfs of some decision statistics even when the support set of the sparse signal is unknown. We apply our detection algorithms with SIC POVM based sequences to a massive random access problem and show their superior performance over conventional Gold codes.

The Han-Kobayashi (HK) scheme achieves the best known achievable rate region for the K user interference channel (IC). Simple HK schemes are HK schemes with Gaussian signaling, no time sharing, and no private-common power splitting. The class of simple HK schemes includes the treating interference as noise (TIN) scheme and schemes that involve various levels of interference decoding and cancellation at each receiver. We derive conditions under which simple HK schemes achieve sum capacity for general K user Gaussian ICs. These results generalize existing sum capacity results for the TIN scheme to the class of simple HK schemes.

We investigate the use of correlated photon pair sources for the improved quantum-level detection of a target in the presence of a noise background. Photon pairs are generated by spontaneous four-wave mixing, one photon from each pair (the herald) is measured locally while the other (the signal) is sent to illuminate the target. Following diffuse reflection from the target, the signal photons are detected by a receiver and non-classical timing correlations between the signal and herald are measured in the presence of a configurable background noise source. Quantum correlations from the photon pair source can be used to provide an enhanced signal-to-noise ratio when compared to a classical light source of the same intensity., Comment: 8 pages, 9 figures

The problem of detecting an odd arm from a set of K arms of a multi-armed bandit, with fixed confidence, is studied in a sequential decision-making scenario. Each arm's signal follows a distribution from a vector exponential family. All arms have the same parameters except the odd arm. The actual parameters of the odd and non-odd arms are unknown to the decision maker. Further, the decision maker incurs a cost for switching from one arm to another. This is a sequential decision making problem where the decision maker gets only a limited view of the true state of nature at each stage, but can control his view by choosing the arm to observe at each stage. Of interest are policies that satisfy a given constraint on the probability of false detection. An information-theoretic lower bound on the total cost (expected time for a reliable decision plus total switching cost) is first identified, and a variation on a sequential policy based on the generalised likelihood ratio statistic is then studied. Thanks to the vector exponential family assumption, the signal processing in this policy at each stage turns out to be very simple, in that the associated conjugate prior enables easy updates of the posterior distribution of the model parameters. The policy, with a suitable threshold, is shown to satisfy the given constraint on the probability of false detection. Further, the proposed policy is asymptotically optimal in terms of the total cost among all policies that satisfy the constraint on the probability of false detection.

We obtain new sum capacity results for the Gaussian many-to-one and one-to-many interference channels in channel parameter regimes where the sum capacity was known only up to a constant gap. Simple Han-Kobayashi (HK) schemes, i.e., HK schemes with Gaussian signaling, no time-sharing, and no common-private power splitting, achieve sum capacity under the channel conditions for which the new results are obtained. To obtain sum capacity results, we show that genie-aided upper bounds match the achievable sum rate of simple HK schemes under certain channel conditions.

This paper is about allocation of an infinitely divisible good to several rational and strategic agents. The allocation is done by a social planner who has limited information because the agents' valuation functions are taken to be private information known only to the respective agents. We allow only a scalar signal, called a bid, from each agent to the social planner. Yang and Hajek [Jour. on Selected Areas in Comm., 2007] as well as Johari and Tsitsiklis [Jour. of Oper. Res., 2009] proposed a scalar strategy Vickrey-Clarke-Groves (SSVCG) mechanism with efficient Nash equilibria. We consider a setting where the social planner desires minimal budget surplus. Example situations include fair sharing of Internet resources and auctioning of certain public goods where revenue maximization is not a consideration. Under the SSVCG framework, we propose a mechanism that is efficient and comes close to budget balance by returning much of the payments back to the agents in the form of rebates. We identify a design criterion for {\em almost budget balance}, impose feasibility and voluntary participation constraints, simplify the constraints, and arrive at a convex optimization problem to identify the parameters of the rebate functions. The convex optimization problem has a linear objective function and a continuum of linear constraints. We propose a solution method that involves a finite number of constraints, and identify the number of samples sufficient for a good approximation., Comment: Accepted for publication in the European Journal of Operational Research (EJOR)

Recognition and identification of unknown targets is a crucial task in surveillance and security systems. Electronic Support Measures (ESM) are one of the most effective sensors for identification, especially for maritime and air--to--ground applications. In typical surveillance systems multiple ESM sensors are usually deployed along with kinematic sensors like radar. Different ESM sensors may produce different types of reports ready to be sent to the fusion center. The focus of this paper is to develop a new architecture for target recognition and identification when non--homogeneous ESM and possibly kinematic reports are received at the fusion center. The new fusion architecture is evaluated using simulations to show the benefit of utilizing different ESM reports such as attributes and signal level ESM data.

In this paper, we analyze the 2-relay multiple-input multiple-output (MIMO) Gaussian diamond channel. We show that a multihopping decode-and-forward with multiple access (MDF-MAC) protocol achieves rates within a constant gap from capacity when a channel parameter $\Delta$ is greater than zero. We also identify the transmit covariance matrices to be used by each relay in the multiple-access (MAC) state of the MDF-MAC protocol. As done for the single-antenna 2-relay Gaussian diamond channel, the channel parameter $\Delta$ is defined to be the difference between the product of the capacities of the links from the source to the two relays and the product of the capacities of the links from the two relays to the destination., Comment: Submitted to ISIT 2016

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 genie-aided 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 \delta > 0, the region where multiple access transmission to one of the receivers is within \delta from sum capacity is determined., Comment: To be presented at ISIT 2015, Hong Kong, China

In this paper, the Gaussian many-to-one X channel, which is a special case of general multiuser X channel, is studied. In the Gaussian many-to-one 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 many-to-one 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. Sum-rate is used as the criterion of optimality for evaluating the strategies. Initially, a $3 \times 3$ many-to-one X channel is considered and three transmission strategies are analyzed. The first two strategies are shown to achieve sum-rate capacity under certain channel conditions. For the third strategy, a sum-rate outer bound is derived and the gap between the outer bound and the achieved rate is characterized. These results are later extended to the $K \times K$ case. Next, a region in which the many-to-one X channel can be operated as a many-to-one IC without loss of sum-rate 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 sum-rate capacity. Subsequently, some implications of the above results to the Gaussian many-to-one IC are discussed. Transmission strategies for the many-to-one IC are formulated and channel conditions under which the strategies achieve sum-rate capacity are obtained. A region where the sum-rate capacity can be characterized to within $K/2-1$ bits is also identified., Comment: Submitted to IEEE Transactions on Information Theory; Revised and updated version of the original draft

We consider two-way relaying in a Gaussian diamond channel, where two terminal nodes wish to exchange information using two relays. A simple baseline protocol is obtained by time-sharing between two one-way protocols. To improve upon the baseline performance, we propose two compute-and-forward (CF) protocols: Compute-and-forward Compound multiple access channel (CF-CMAC) and Compute-and-forward-Broadcast (CF-BC). These protocols mix the two flows through the two relays and achieve rates better than the simple time-sharing protocol. We derive an outer bound to the capacity region that is satisfied by any relaying protocol, and observe that the proposed protocols provide rates close to the outer bound in certain channel conditions. Both the CF-CMAC and CF-BC protocols use nested lattice codes in the compute phases. In the CF-CMAC protocol, both relays simultaneously forward to the destinations over a Compound Multiple Access Channel (CMAC). In the simpler CF-BC protocol's forward phase, one relay is selected at a time for Broadcast Channel (BC) transmission depending on the rate-pair to be achieved. We also consider the diamond channel with direct source-destination link and the diamond channel with interfering relays. Outer bounds and achievable rate regions are compared for these two channels as well. Mixing of flows using the CF-CMAC protocol is shown to be good for symmetric two-way rates., Comment: 8 pages, 7 figures Proceedings of 51st Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, USA, Oct 2013

We consider a data aggregating wireless network where all nodes have data to send to a single destination node, the sink. We consider a linear placement of nodes with the sink at one end. The nodes communicate directly to the sink (single hop transmission) and we assume that the nodes are scheduled one at a time by a central scheduler (possibly the sink). The wireless nodes are power limited and our network objective (notion of fairness) is to maximize the minimum throughput of the nodes subject to the node power constraints. In this work, we consider network designs that permit adapting node transmission time, node transmission power and node placements, and study cross- layer strategies that seek to maximize the network throughput. Using simulations, we characterize the performance of the dif- ferent strategies and comment on their applicability for various network scenarios., Comment: 5 pages

We consider allcast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not consist of all the nodes, the remaining nodes act as relays. The nodes are connected by undirected links whose capacities are independent and identically distributed random variables. We study the asymptotics of the capacity region (with network coding) in the limit of a large number of nodes, and show that the normalized sum rate converges to a constant almost surely. We then provide a decentralized push-pull algorithm that asymptotically achieves this normalized sum rate without network coding., Comment: 13 pages, extended version of paper presented at the IEEE International Symposium on Information Theory (ISIT) 2012, minor revision to text to address review comments, to appear in IEEE Transactions in information theory

In an M x N interference network, there are M transmitters and N receivers with each transmitter having independent messages for each of the 2^N -1 possible non-empty subsets of the receivers. We consider the 2 x 2 interference network with 6 possible messages, of which the 2 x 2 interference channel and X channel are special cases obtained by using only 2 and 4 messages respectively. Starting from an achievable rate region similar to the Han-Kobayashi region, we obtain an achievable sum rate. For the Gaussian interference network, we determine which of the 6 messages are sufficient for maximizing the sum rate within this rate region for the low, mixed, and strong interference conditions. It is observed that 2 messages are sufficient in several cases., Comment: Theorem 4 in previous version removed. See https://arxiv.org/abs/1505.06317 for updated results

We consider a three-node half-duplex Gaussian relay network where two nodes (say $a$, $b$) want to communicate with each other and the third node acts as a relay for this twoway communication. Outer bounds and achievable rate regions for the possible rate pairs $(R_a, R_b)$ for two-way communication are investigated. The modes (transmit or receive) of the halfduplex nodes together specify the state of the network. A relaying protocol uses a specific sequence of states and a coding scheme for each state. In this paper, we first obtain an outer bound for the rate region of all achievable $(R_a,R_b)$ based on the half-duplex cut-set bound. This outer bound can be numerically computed by solving a linear program. It is proved that at any point on the boundary of the outer bound only four of the six states of the network are used. We then compare it with achievable rate regions of various known protocols. We consider two kinds of protocols: (1) protocols in which all messages transmitted in a state are decoded with the received signal in the same state, and (2) protocols where information received in one state can also be stored and used as side information to decode messages in future states. Various conclusions are drawn on the importance of using all states, use of side information, and the choice of processing at the relay. Then, two analytical outer bounds (as opposed to an optimization problem formulation) are derived. Using an analytical outer bound, we obtain the symmetric capacity within 0.5 bits for some channel conditions where the direct link between nodes a and b is weak., Comment: Presented at Allerton Conference on Communication, Control and Computing 2012

In conventional target tracking systems, human operators use the estimated target tracks to make higher level inference of the target behaviour/intent. This paper develops syntactic filtering algorithms that assist human operators by extracting spatial patterns from target tracks to identify suspicious/anomalous spatial trajectories. The targets' spatial trajectories are modeled by a stochastic context free grammar (SCFG) and a switched mode state space model. Bayesian filtering algorithms for stochastic context free grammars are presented for extracting the syntactic structure and illustrated for a ground moving target indicator (GMTI) radar example. The performance of the algorithms is tested with the experimental data collected using DRDC Ottawa's X-band Wideband Experimental Airborne Radar (XWEAR).

Wireless networks with multiple nodes that relay information from a source to a destination are expected to be deployed in many applications. Therefore, understanding their design and performance under practical constraints is important. In this work, we propose and study three multihopping decode and forward (MDF) protocols for multistage half-duplex relay networks with no direct link between the source and destination nodes. In all three protocols, we assume no cooperation across relay nodes for encoding and decoding. Numerical evaluation in illustrative example networks and comparison with cheap relay cut-set bounds for half-duplex networks show that the proposed MDF protocols approach capacity in some ranges of channel gains. The main idea in the design of the protocols is the use of coding in interference networks that are created in different states or modes of a half-duplex network. Our results suggest that multistage half-duplex relaying with practical constraints on cooperation is comparable to point-to-point links and full-duplex relay networks, if there are multiple non-overlapping paths from source to destination and if suitable coding is employed in interference network states., Comment: 5 pages, submitted to ISIT 2010

Dirty paper coding (DPC) refers to methods for pre-subtraction of known interference at the transmitter of a multiuser communication system. There are numerous applications for DPC, including coding for broadcast channels. Recently, lattice-based coding techniques have provided several designs for DPC. In lattice-based DPC, there are two codes - a convolutional code that defines a lattice used for shaping and an error correction code used for channel coding. Several specific designs have been reported in the recent literature using convolutional and graph-based codes for capacity-approaching shaping and coding gains. In most of the reported designs, either the encoder works on a joint trellis of shaping and channel codes or the decoder requires iterations between the shaping and channel decoders. This results in high complexity of implementation. In this work, we present a lattice-based DPC scheme that provides good shaping and coding gains with moderate complexity at both the encoder and the decoder. We use a convolutional code for sign-bit shaping, and a low-density parity check (LDPC) code for channel coding. The crucial idea is the introduction of a one-codeword delay and careful parsing of the bits at the transmitter, which enable an LDPC decoder to be run first at the receiver. This provides gains without the need for iterations between the shaping and channel decoders. Simulation results confirm that at high rates the proposed DPC method performs close to capacity with moderate complexity. As an application of the proposed DPC method, we show a design for superposition coding that provides rates better than time-sharing over a Gaussian broadcast channel., Comment: 5 pages, submitted to ISIT 2010