We study the low SNR scaling of the non-coherent secret-key agreement capacity over a reciprocal, block-fading channel. For the restricted class of strategies, where one of the nodes is constrained to transmit pilot-only symbols, we show that the secret-key capacity scales as SNR ·log T if T ≤ 1/SNR, where T denotes the coherence period, and as SNR·log(1/SNR) otherwise. Our upper bound is inspired by the genie-aided argument of Borade and Zheng (IT-Trans 2010). Our lower bound is based on bursty communication, channel training, and secret message transmission.
We study secret-key agreement over a non-coherent block-fading multiple input multiple output (MIMO) wiretap channel. We give an achievable scheme based on training and source emulation and analyze the rate in the high SNR regime. Based on this analysis we find the optimal number of antennas to use for training. Our main result is that if the sum of the number of antennas at Alice and Bob is larger than the coherence time of the channel, the achievable rate does not depend on the number of antennas at Eve. In this case source emulation is not needed, and using only training is optimal. We also consider the case when there is no public channel available. In this case we show that secret-key agreement is still possible by using the wireless channel for discussion, giving the same number of secure degrees of freedom as in the case with a public channel.
We consider transmission over a binary erasure wiretap channel using the code construction method introduced by Rathi et al. based on two edge type Low-Density Parity-Check (LDPC) codes and the coset encoding scheme. By generalizing the method of computing conditional entropy for standard LDPC ensembles introduced by Méasson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity.
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.
The integration of multiple services such as the transmission of private, common, and confidential messages at the physical layer is becoming important for future wireless networks in order to increase spectral efficiency. In this paper, bidirectional relay networks are considered, in which a relay node establishes bidirectional communication between two other nodes using a decode-and-forward protocol. In the broadcast phase, the relay transmits additional common and confidential messages, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. This channel generalizes the broadcast channel with receiver side information considered by Kramer and Shamai. Low complexity polar codes are constructed that achieve the capacity region of both the degraded symmetric BBC, and the BBC with common and confidential messages. The use of polar codes allows an intuitive interpretation of how to incorporate receiver side information and secrecy constraints as different sets of frozen bits at the different receivers for an optimal code design. In order to show that the constructed codes achieve capacity, a tighter bound on the cardinality of an auxiliary random variable used in the converse is found using a method by Salehi.
We consider the bidirectional broadcast channel with common and confidential messages. We show that polar codes achieve the capacity of binary input symmetrical bidirectional broadcast channels with confidential messages, if one node's channel is a degraded version of the other node's channel. We also find a new bound on the cardinality of the auxiliary random variable in this setup.
A scenario of distributed sensing for networked control systems is considered and a new approach to distributed sensing and transmission is presented. The state process of a scalar first order linear time invariant dynamical system is sensed by a network of wireless sensors, which then instantaneously transmit their measurements to a remotely situated control unit over parallel Gaussian channels. The control unit aims to stabilize the system in mean square sense. The proposed non-linear delay-free sensing and transmission strategy is compared with the well-known amplify-and-forward strategy, using the LQG control cost as a figure of merit. It is demonstrated that the proposed nonlinear scheme outperforms the best linear scheme even when there are only two sensors in the network. The proposed sensing and transmission scheme can be implemented with a reasonable complexity and it is shown to be robust to the uncertainties in the knowledge of the sensors about the statistics of the measurement noise and the channel noise.
We illustrate how channel optimized vector quantization (COVQ) can be used for channels with both bit-errors and bit-erasures. First, a memoryless channel model is presented, and the performance of COVQ's trained for this channel is evaluated for an i.i.d. Gaussian source. Then, the new method is applied in implementing an error-robust sub-band image coder, and we present image results that illustrate the resulting performance. Our experiments show that the new approach is able to outperform a traditional scheme based on separate source and channel coding.
A new design approach for multiple description vector quantizers over more than two channels is presented. The design is inspired by the concept of channel optimized vector quantization. While most previous works have split the decoder into several independent entities, identifying the appropriate channel model makes it straightforward to implement the multiple description design problem using only one decoder. Our simulation results compare systems with 2, 4 and 8 channels. We demonstrate significant gains over previous designs, as well as over a benchmark scheme based on separate quantization and forward erasure-correcting error control.
A new design approach for multiple description coding, based on multi-stage vector quantizers, is presented. The design is not limited to systems with two descriptions, but is also well suited for the n-descriptions case. Inspired by the concept of channel optimized vector quantization, the design can easily be tailored to suit different erasure channels, e.g. packet erasure channels with memory (burst-losses). The optimization procedure used in the design takes a sample-iterative approach. All stage codebooks; are updated simultaneously for each vector in the training database. The resulting algorithm has the behaviour of a simulated annealing algorithm, with several good properties, e.g. it usually provides codebooks with good index assignments. Image results are presented for systems with 2 and 4 channels. The image coder is based on a subband transform followed by 64-dimensional vector quantization, to illustrate the capacity of the design to handle large problem sizes.
Fast analog to digital conversion with only one bit per sample does not only make high sampling rates possible but also reduces the required hardware complexity. For short data buffers or block lengths, it has been shown that tone frequency estimators can be implemented by a simple table look-up. In this paper we present an analysis of such tables using the Hadamard transform. As an outcome of the analysis, we propose a class of nonlinear estimators of low complexity. Their performance is evaluated using numerical simulations. Comparisons are made with the proper Cramer-Rao bound and with the table look-up approach.
Encoder-decoder design is considered for a closed-loop scalar control system with feedback transmitted over a binary symmetric channel. We propose an iterative procedure which can jointly optimize adaptive encoder-decoder pairs for a certainly equivalence controller. The goal is to minimize a design criterion, in particular, the linear quadratic (LQ) cost function over a finite horizon. The algorithm leads to a practically feasible design of time-varying non-uniform encoding and decoding. Numerical results demonstrate the promising performance obtained by employing the proposed iterative optimization algorithm.
The problem of allocating communication resources to multiple plants in a networked control system is investigated. In the presence of a shared communication medium, a total transmission rate constraint is imposed. For the purpose of optimizing the rate allocation to the plants over a finite horizon, two objective functions are considered. The first one is a single-objective function, and the second one is a multi-objective function. Because of the difficulty to derive the closed-form expression of these functions, which depend on the instantaneous communication rate, an approximation is proposed by using high-rate quantization theory. It is shown that the approximate objective functions are convex in the region of interest both in the scalar case and in the multi-objective case. This allows to establish a linear control policy given by the classical linear quadratic Gaussian theory as function of the channel. Based on this result, a new complex relation between the control performance and the channel error probability is characterized.
In this paper, we study the iterative optimization of the encoder-controller pair for closed-loop control of a multi-dimensional plant over a noisy discrete memoryless channel. With the objective to minimize the expected linear quadratic cost over a finite horizon, we propose a joint design of the sensor measurement quantization, channel error protection, and optimal controller actuation. It was shown in our previous work that despite this optimization problem is known to be hard in general, an iterative design procedure can be derived to obtain a local optimal solution. However, in the vector case, optimizing the encoder for a fixed controller is in general not practically feasible due to the curse of dimensionality. In this paper, we propose a novel approach that uses the approximate dynamic programming (ADP) to implement a computationally feasible encoder updating policy with promising performance. Especially, we introduce encoder updating rules adopting the rollout approach. Numerical experiments are carried out to demonstrate the performance obtained by employing the proposed iterative design procedure and to compare it with other relevant schemes.
In this paper, we consider the problem of the joint optimization of encoder-controller for closed-loop control with state feedback over a binary-input Gaussian channel (BGC). The objective is to minimize the expected linear quadratic cost over a finite horizon. Thisencoder-controller optimization problem is hard in general, mostly because of the curse of dimensionality. The result of this paper is a synthesis technique for a computationally feasible suboptimal controller which exploits both the soft and hard information of thechannel outputs. The proposed controller is efficient in the sense that it embraces measurement quantization, error protection and control over a finite-input infinite-output noisy channel. How to effectively implement this controller is also addressed in the paper. In particular, this is done by using Hadamard techniques. Numerical experiments are carried out to verify the promising gain offered by the combined controller, in comparison to the hard-information-based controller.
Optimal rate allocation in a networked control system with limited communication resources is instrumental to achieve satisfactory overall performance. In this paper, a practical rate allocation technique for state estimation in linear dynamic systems over a noisy channel is proposed. The method consists of two steps: (i) the overall distortion is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize the overall distortion is solved by using Lagrange duality. Monte Carlo simulations illustrate the proposed scheme, which is shown to have good performance when compared to arbitrarily selected rate allocations.
Optimal rate allocation in a networked control system with highly limited communication resources is instrumental to achieve satisfactory overall performance. In this paper, we propose a rate allocation technique for state feedback control in linear dynamic systems over a noisy channel. Our method consists of two steps: (i) the overall distortion is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize the overall distortion is solved. We show that a non-uniform quantization is in general the best strategy for state feedback control over noisy channels. Monte Carlo simulations illustrate the proposed scheme, which is shown to have good performance compared to arbitrarily selected rate allocations.
Utility maximization in networked control systems (NCSs) is difficult in the presence of limited sensing and communication resources. In this paper, a new communication rate optimization method for state feedback control over a noisy channel is proposed. Linear dynamic systems with quantization errors, limited transmission rate, and noisy communication channels are considered. The most challenging part of the optimization is that no closed-form expressions are available for assessing the performance and the optimization problem is nonconvex. The proposed method consists of two steps: (i) the overall NCS performance measure is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize a weighted quadratic objective function is solved. The proposed method is applied to the problem of state feedback control and the problem of state estimation. Monte Carlo simulations illustrate the performance of the proposed rate allocation. It is shown numerically that the proposed method has better performance when compared to arbitrarily selected rate allocations. Also, it is shown that in certain cases nonuniform rate allocation can outperform the uniform rate allocation, which is commonly considered in quantized control systems, for feedback control over noisy channels.
To achieve satisfactory overall performance, optimal rate allocation in a networked control system with highly limited communication resources is instrumental. In this paper, a rate allocation technique for state feedback control in linear dynamic systems over a noisy channel is proposed. The method consists of two steps: (i) the overall cost is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize the overall distortion is solved. It is shown that a non-uniform quantization is in general the best strategy for state feedback control over noisy channels. Monte Carlo simulations illustrate the proposed scheme, which is shown to have good performance when compared to arbitrarily selected rate allocations.
We study a closed-loop scalar control system with feedback transmitted over a discrete noisy channel. For this problem, we propose a joint design of the state measurement quantization, protection against channel errors, and control. The goal is to minimize a linear quadratic cost function over a finite horizon. In particular we focus on a special case where we verify that certainty equivalence holds, and for this case we design joint source-channel encoder and decoder/estimator pairs. The proposed algorithm leads to a practically feasible design of time-varying non-uniform quantization and control. Numerical results demonstrate the promising performance obtained by employing the proposed iterative optimization algorithm.
Bandwidth limitations and energy constraints set severe restrictions on the design of control systems that utilize wireless sensor and actuator networks. It is common in these systems that a sensor node needs not be continuously monitored, but communicates to the controller only at certain instances when it detects a disturbance event. In this paper, such a scenario is studied and particular emphasis is on efficient utilization of the shared communication resources. Encoder-decoder design for an event-based control system with the plant affected by pulse disturbances is considered. A new iterative procedure is proposed which can jointly optimize encoder-decoder pairs for a certainty equivalent controller. The goal is to minimize a design criterion, in particular, a linear quadratic cost over a finite horizon. The algorithm leads to a feasible design of time-varying non-uniform encoder-decoder pairs. Numerical results demonstrate significant improvements in performance compared to a system using uniform quantization.
We study a closed-loop control system with state feedback transmitted over a noisy discrete memoryless channel. With the objective to minimize the expected linear quadratic cost over a finite horizon, we propose a joint design of the sensor measurement quantization, channel error protection, and controller actuation. It is argued that despite that this encoder-controller optimization problem is known to be hard in general, an iterative design procedure can be derived in which the controller is optimized for a fixed encoder, then the encoder is optimized for a fixed controller, etc. Several properties of such a scheme are discussed. For a fixed encoder, we study how to optimize the controller given that full or partial side-information is available at the encoder about the symbols received at the controller. It is shown that the certainty equivalence controller is optimal when the encoder is optimal and has full side-information. For a fixed controller, expressions for the optimal encoder are given and implications are discussed for the special cases when process, sensor, or channel noise is not present. Numerical experiments are carried out to demonstrate the performance obtained by employing the proposed iterative design procedure and to compare it with other relevant schemes.
We study a closed-loop control system with feedback transmitted over a noisy discrete memoryless channel. We design encoder-controller pairs that jointly optimize the sensor measurement quantization, protection against channel errors, and control. The designgoal is to minimize an expected linear quadratic cost over a finite horizon. As a result of deriving optimality criteria for this problem, we present new results on the validity of theseparation principle subject to certain assumptions. More precisely, we show that the certainty equivalence controller is optimal when the encoder is optimal and has full side-information about the symbols received at the controller. We then use this result to formulate tractable design criteria in the general case. Finally, numerical experiments are carried out to demonstrate the performance obtained by various design methods.
We study a closed-loop multivariable control system with sensor feedback transmitted over a discrete noisy channel. For this problem, we propose a joint design of the state measurement quantization, protection against channel errors, and control. The proposed algorithm leads to a practically feasible design of time-varying non-uniform encoding and control. Numerical results demonstrate the performance obtained by employing the proposed iterative optimization algorithm.
Full-duplex communications have the potential to almost double the spectralefficiency. To realize such a potentiality, the signal separation at base station’s antennasplays an essential role. This paper addresses the fundamentals of such separationby proposing a new smart antenna architecture that allows every antenna to beeither shared or separated between uplink and downlink transmissions. The benefitsof such architecture are investigated by an assignment problem to optimally assignantennas, beamforming and power to maximize the weighted sum spectral efficiency.We propose a near-to-optimal solution using block coordinate descent that divides theproblem into assignment problems, which are NP-hard, a beamforming and powerallocation problems. The optimal solutions for the beamforming and power allocationare established while near-to-optimal solutions to the assignment problems are derivedby semidefinite relaxation. Numerical results indicate that the proposed solution isclose to the optimum, and it maintains a similar performance for high and low residualself-interference powers. With respect to the usually assumed antenna separationtechnique and half-duplex transmission, the sum spectral efficiency gains increase withthe number of antennas. We conclude that our proposed smart antenna assignment forsignal separation is essential to realize the benefits of multiple antenna full-duplexcommunications.
We investigate the problem of sharing the outcomes of a parametric source with an untrusted party while ensuring the privacy of the parameters. We propose privacy mechanisms which guarantee parameter privacy under both Bayesian statistical as well as information-theoretic privacy measures. The properties of the proposed mechanisms are investigated and the utility-privacy trade-off is analyzed.
We investigate the problem of sharing (communi-cating) the outcomes of a memoryless source when some of its statistical parameters must be kept private. Privacy is measured in terms of the Bayesian statistical risk according to a desired loss function while the quality of the reconstruction is measured by the average per-letter distortion. We first bound -uniformly over all possible estimators- the expected risk from below. This information-theoretic bound depends on the mutual information between the parameters and the disclosed (noisy) samples. We then present an achievable scheme that guarantees an upper bound on the average distortion while keeping the risk above a desired threshold, even when the length of the sample increases.
We investigate the behavior of the mutual information between two Boolean functions of correlated binary strings. The covariance of these functions is found to be a crucial parameter in the aforementioned mutual information. We then apply this result in the analysis of a specific privacy problem where a user observes a random binary string. Under particular conditions, we characterize the optimal strategy for communicating the outcomes of a function of said string while preventing to leak any information about a different function.
Remote stabilization of linear dynamical systems over Gaussian networks is studied. Two linear time invariant systems (plants) with arbitrary distributed initial states are monitored by two separate sensors. The sensors communicate their measurements to two remotely situated controllers over a Gaussian interference, possibly with the assistance from a relay node. The common goal of the sensors, relay, and controllers is to stabilize the plants in mean-square sense. An optimized linear delay-free sensing and control scheme is proposed and sufficient conditions for mean-square stability are derived. These conditions reveal the relationship between plants' stability and communication channel parameters. It is shown that the proposed linear scheme can significantly outperform the existing estimation based control scheme in multi-user Gaussian networks.
A transmission scheme for mean square stabilization of two linear systems over a Gaussian interference relay channel is studied. A delay-free linear sensing and control strategy is proposed and an achievable stability region is derived. It shows that the stability region can be significantly enlarged by deploying a relay node in such a multi-user Gaussian channels. Furthermore we observe that the separation structure between estimation and control is inadequate in high interference regime.
The remote stabilization of a first order linear plant over a wireless channel is studied. The plant is assumed to have an arbitrary distributed initial state and the wireless channel between the plant's sensor and the controller is modeled as a white Gaussian channel subject to an external interference signal. In order to combat the interference a dedicated sensor (relay) node is deployed adjacent to the interferer, which relays the interference information to both the plant's sensor and the controller. The sensor and the controller utilize this information to mitigate interference. We use delay-free linear sensing and control scheme in order to derive sufficient conditions for mean square stability. The achievable stability region significantly enlarges with the relay assisted interference cancelation scheme. Moreover the effect of interference can be completely eliminated if the encoder knows all the future values of the interference.
We consider an extension of the cognitive radio channel model in which the secondary transmitter has to obtain (“learn”) the primary message in a first phase rather than having non-causal knowledge of it. We propose an achievable rate region that combines elements of decode-and-forward relaying with coding for the pure cognitive radio channel model. Moreover, we find the choice of parameters that maximize the secondary rate under a primary rate constraint. Finally, we compare numerically the performance of our system to that of an underlay scheme that combines beamforming, rate splitting, and successive decoding. We observe that although the overlay design provides higher rates, the losses due to the first phase are quite severe. In fact, for the considered scenarios, cleverly designed underlay schemes can provide comparable performance.
We consider the symmetric discrete memoryless relay channel with orthogonal receiver components and show that polar codes are suitable for decode-and-forward and compress-and-forward relaying. In the first case we prove that polar codes are capacity achieving for the physically degraded relay channel; for stochastically degraded relay channels our construction provides an achievable rate. In the second case we construct sequences of polar codes that achieve the compress-and-forward rate by nesting polar codes for source compression into polar codes for channel coding. In both cases our constructions inherit most of the properties of polar codes. In particular, the encoding and decoding algorithms and the bound on the block error probability O(2 (N beta)) which holds for any 0 < beta < 1/2.
We construct polar codes for binary relay channels with orthogonal receiver components. We show that polar codes achieve the cut-set bound when the channels are symmetric and the relay-destination link supports compress-and-forward relaying based on Slepian-Wolf coding. More generally, we show that a particular version of the compress-and-forward rate is achievable using polar codes for Wyner-Ziv coding. In both cases the block error probability can be bounded as O(2-Nβ) for 0 < β < 1/2 and sufficiently large block length N.
We propose a new code design for compress-and-forward relaying over bandlimited relay-to-destination channels. The main contribution of this paper is a code design based on joint (source-channel) coding and modulation that uses the correlation between the observations at the relay and the destination as protection against channel errors. This allows for relay nodes with reduced complexity, shifting most of the processing requirements to the destination node. Moreover, by using scalar quantizers with an entropy constraint our system provides remarkable performance in channel conditions where neither amplify-and-forward nor compress-and-forward efficiently exploit the presence of a relay node. Simulation results confirm the benefits of our proposed system.
We study the problem of controlling the interference created to an external observer by a communication processes. We model the interference in terms of its type (empirical distribution), and we analyze the consequences of placing constraints on the admissible type. Considering a single interfering link, we characterize the communication-interference capacity region. Then, we look at a scenario where the interference is jointly created by two users allowed to coordinate their actions prior to transmission. In this case, the tradeoff involves communication and interference as well as coordination. We establish an achievable communication-interference region and show that efficiency is significantly improved by coordination.
We propose a new compress-and-forward implementation for the relay channel based on joint source-channel coding techniques. The relay performs scalar quantization of its observation in combination with a redundant index mapping. Our system utilizes the correlation between the quantized signal and the direct-link observation of the transmitted symbols as redundancy for error protection on the relay-to-destination link. In order to fully exploit this correlation the destination requires iterative decoding to recover the quantized observation sent by the relay. Once regenerated, this quantized signal is optimally combined with the direct-link observation to decode the message conveyed by the source. By quantizing the observed signal itself rather than a measure on the reliability of the information bits (e.g. a posteriori probabilities from a decoder), and by using digital communication methods on the relay-to-destination link our system yields superior performance to that of amplify-and-forward, decode-and-forward and previous implementations of compress-and-forward based on soft decoding.
We consider coordination in cascade networks and construct sequences of polar codes that achieve any point in a special region of the empirical coordination capacity region. Our design combines elements of source coding to generate actions with the desired type with elements of channel coding to minimize the communication rate. Moreover, we bound the probability of malfunction of a polar code for empirical coordination. Possible generalizations and open problems are discussed.
We study the fundamental relationship between two relevant quantities in compressive sensing: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/ log n (m being the number of measurements and n the dimension of the sparse signal), and the mean square estimation error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total signal power when the sparsity level is fixed. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean square error. This tradeoff is achievable using a two-step approach: first support set recovery, then estimation of the active components. Finally, for both deterministic and random signals, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery.
For compressive sensing, we derive achievable performance guarantees for recovering partial support sets of sparse vectors. The guarantees are determined in terms of the fraction of signal power to be detected and the measurement rate, defined as a relation between the dimensions of the measurement matrix. Based on this result we derive a tradeoff between the measurement rate and the mean square error, and illustrate it by a numerical example.
This letter considers optimal transmit beamforming for a sub-connected large-scale MISO system with RF chain and per-antenna power constraints. The system is configured such that each RF chain serves a group of antennas. For the hybrid scheme, necessary and sufficient conditions to design the optimal digital and analog precoders are provided. It is shown that, in the optimum, the optimal phase shift at each antenna has to match the channel coefficient and the phase of the digital precoder. In addition, an iterative algorithm is provided to find the optimal power allocation. We study the case where the power constraint on each RF chain is smaller than the sum of the corresponding per-antenna power constraints. Then, the optimal power is allocated based on two properties: each RF chain uses full power and if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna.
We consider multiple-input single-output (MISO) Gaussian channels with joint sum and per-antenna power constraints. A closed-form solution of the optimal beamforming vector is derived which achieves the maximal transmission rate. The result shows that if the sum power constraint only optimal power allocation violates a per-antenna power constraint then the joint power constraint optimal power allocation is at the intersection of the sum power constraint and the per-antenna power constraints.
This paper provides the necessary conditions to design precoding matrices for massive MIMO systems with a sub-connected architecture, RF power constraints and per-antenna power constraints. The system is configured such that each RFchain serves a group of antennas. The necessary condition to design the digital precoder is established based on a generalized water-filling and joint sum and per-antenna optimal power allocation solution, while the analog precoder is based on a per-antenna power allocation solution only. We study the analytically most interesting case where the power constraint on the RF chain is smaller than the sum of the corresponding per-antenna power constraints. For this, the optimal power is allocated based on two properties: Each RF chain uses full power and if the optimal power allocation of the unconstraint problem violates a per-antenna power constraint then it is optimal to allocate the maximal power for that antenna.
This paper considers the optimal transmit strategy for multi-antenna bidirectional broadcast channels with per-antenna power constraints. First, an equivalent formulation of the weighted rate sum maximization problem is provided. This allows us to come up with an effective solution to characterize the boundary of the capacity region which relies on the weighted rate sum optimal rate pair. To that end, an iterative algorithm to find the optimal transmit strategy is derived, the convergence to the optimum is proved, and a closed-form solution of the corresponding off-diagonal elements of the optimal transmit strategy is provided. Further, we provide a parametrization of the curved section of the capacity region. Finally, the theoretical results and algorithm performance are illustrated by numerical examples.
In this paper, we study an optimal transmit strategy for multiple-input single-output (MISO) Gaussian channels with joint sum and per-antenna power constraints. We study in detail the interesting case where the sum of the per-antenna power constraints is larger than sum power constraint. A closed-form characterization of an optimal beamforming strategy is derived.It is shown that we can always find an optimal beamforming transmit strategy that allocates the maximal sum power with phases matched to the complex channel coefficients. The main result is a simple recursive algorithm to compute the optimal power allocation. Whenever the optimal power allocation of the corresponding problem with sum power constraint only exceeds per-antenna power constraints, it is optimal to allocate maximal per-antenna power to those antennas to satisfy the per-antenna power constraints. The remaining power is divided amongst the other antennas whose optimal allocation follows from a reduced joint sum and per-antenna power constraints problem of smaller channel coefficient dimension and reduced sum power constraint. Finally, the theoretical results are illustrated by numerical examples.
In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in reducing the average complexity and hence the latency of the decoder. We numerically validate the approach through Monte Carlo simulations.
Stringent constraints on both reliability and latency must be guaranteed in ultra-reliable low-latency communication (URLLC). To fulfill these constraints with computationally constrained receivers, such as low-budget IoT receivers, optimal transmission parameters need to be studied in detail. In this paper, we introduce a multi-objective optimization framework for the optimal design of URLLC in the presence of decoding complexity constraints. We consider transmission of short-blocklength codewords that are encoded with linear block encoders, transmitted over a binary-input AWGN channel, and finally decoded with order-statistics (OS) decoder. We investigate the optimal selection of a transmission rate and power pair, while satisfying the constraints. For this purpose, a multi-objective optimization problem (MOOP) is formulated. Based on the empirical model that accurately quantifies the trade-off between the performance of an OS decoder and its computational complexity, the MOOP is solved and the Pareto boundary is derived. In order to assess the overall performance among several Pareto-optimal transmission pairs, two scalarization methods are investigated. To exemplify the importance of the MOOP, a case study on a battery-powered communication system is provided. It is shown that, compared to the classical fixed rate-power transmissions, the MOOP provides the optimum usage of the battery and increases the energy efficiency of the communication system while maintaining the constraints.