Phase-incoherent feedback communication

In light of recent results by Verdú and Han on channel capacity, we examine three problems: the strong converse condition to the channel coding.theorem, the capacity of arbitrary channels with feedback and the Neyman‐Pearson hypothesis testing type‐II error exponent. It is first remarked that the strong converse condition holds if and only if the sequence of normalized channel information densities converges in probability to a constant. Examples illustrating this condition are provided. A general formula for the capacity of arbitrary channels with output feedback is then obtained. Finally, a general expression for the Neyman‐Pearson type‐II error exponent based on arbitrary observations subject to a constant bound on the type‐I error probability is derived.

In this paper, we study the problem of stabilizability of LTI systems over both the forward (from the controller to the plant) and feedback (from the sensor to the controller) channel. We adopt the additive white noise (AWN) channel with a prescribed power constraint as our channel model. For first order systems, we derive explicitly the necessary and sufficient conditions for stabilizability and show the tradeoff between the minimum signal-to-noise ratio (SNR) required for the forward and feedback channel. We also show explicitly that the use of two-parameter controller in this problem assumes better performance.

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive an exact analytical expression for the random coding error exponent, which provides significant insight regarding the ultimate limits to communications through Nakagami-m fading channels. An important fact about this error exponent is that it determines the behavior of error probability in terms of the transmission rate and the code length that reflects the coding complexity required to achieve a certain level of reliability. Moreover, from the derived analytical expression, we can easily compute the necessary codeword length without extensive Monte-Carlo simulation to achieve a predefined upper bound for error probability at a rate below the channel capacity. We also improve the random coding bound by expurgating bad codewords from the code ensemble, since random coding error exponent is determined by selecting codewords independently according to the input distribution where good and bad codewords contribute equally to the overall average error probability. Finally, we derive exact analytical expressions for the cutoff rate, critical rate, and expurgation rate and verify the analytical expressions via Monte-Carlo simulation.

Previously, it has been shown that more feedback links may help to achieve larger finite blocklength rates of the Gaussian relay channel (GRC). However, this is only built on the idealistic assumption that the feedback channels are noise free. In this paper, we revisit the GRC with feedback by considering the situation that the feedback channels are also corrupted by additive white Gaussian noises. For given coding blocklength and decoding error probability, achievable rates of our proposed schemes are characterized. Numerical results show that comparing with those schemes of the same model without using feedback, there may still exist rate gain even the feedback channels are corrupted by noises. Besides this, we also show that comparing with the existing feedback scheme for the GRC with one noise-free feedback link, two noisy feedback links still bring rate gain for some cases.

The use of codes in forward error correction and decision feedback schemes is analysed. Various comparisons of the two types of error control scheme are undertaken when finite and infinite repetitions are possible and when the feedback channel can be considered noisy or noiseless. These comparisons are based on the consideration of both the average information bit error probability and transmission efficiency to obtain the overall effectiveness of the error control schemes.

The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -user cyclic Z-interference channel models a situation in which the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> th transmitter causes interference only to the ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -1)th receiver in a cyclic manner, e.g., the first transmitter causes interference only to the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> th receiver. The impact of noiseless feedback on the capacity of this channel is studied by focusing on the Gaussian cyclic Z-interference channel. To this end, the symmetric feedback capacity of the linear shift deterministic cyclic Z-interference channel is completely characterized for all interference regimes. Using insights from the linear deterministic channel model, the symmetric feedback capacity of the Gaussian cyclic Z-interference channel is characterized up to within a constant number of bits. As a byproduct of the constant gap result, the symmetric generalized degrees of freedom with feedback for the Gaussian cyclic Z-interference channel are also characterized. These results highlight that the symmetric feedback capacities for both linear and Gaussian channel models are in general functions of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> , the number of users. Furthermore, the capacity gain obtained due to feedback decreases as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> increases.

This paper investigates the event-triggered predictive control problem of networked control systems (NCSs) with the event-triggered mechanism adopted both in the forward and feedback channels to save the network resources. The transmition time instants of states are determined by an event-triggered mechanism, which contains a dynamic reference state, in the feedback channel. Combination of the event-triggered mechanism and the networked predictive control approach is employed to estimate states as well as future control input sequences of the system in the forward channel. The derived estimate state error system of the networked event-triggered predictive control system is proven to be uniformly globally asymptotic stable. Simulation results are provided to demonstrate the effectiveness and applicability of the proposed event-triggered predictive control scheme.

The paper is concerned with an improved predictive control method of NCSs (Networked Control Systems) with random time delay and data dropout. The design of networked control system we proposed is based on Scenario-Based Networked Control (SBNC). Through this method the NCSs' performance is relative with an equivalent data-dropout probability. In this paper, the improved method is applied on the linear systems, and the network is in both forward and feedback channels that is more realistic. The buffer in feedback channel makes the system equivalent to a system with an extra forward delay, and the feedback channel has no delay. The simulation on the ball and beam system verifies the effectiveness and rationality of the proposed control algorithm. Besides, the comparison between a different predictive method and this improved one is achieved, and the latter one shows better tracking properties even when the network is very bad. The effects of the parameters are also considered in the simulation.

An intermittent on-off noiseless feedback scheme for binary communication over the slow- and fast-fading Rayleigh channels is proposed and analyzed. At high energy-to-noise ratios, doubling the number of feedback iterations yields a 3-dB power saving for the slowly fading channel. Power savings ranging from 1 dB for one feedback iteration to 9 dB for 16 iterations are typical for the fast-fading model. Also for the fast-fading model, by picking the optimum number of forward transmissions for each value of energy-to-noise ratio, the best achievable performance requires approximately 7.5 dB more energy than the minimum predicted by the rate-distortion bound. Also presented is a feedback communication system for wide-sense stationary, uncorrelated-scatterer, fading, and dispersive forward and feedback channels. The model used for both forward and feedback channels is Kennedy's. Upper and lower bounds on the error probability for block orthogonal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> -ary communication are presented for this system.

8 - Error-correcting codes

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

The relationship between weak convergence of channel probability measures, channel capacity, and error probability of block codes is examined for memoryless channels with general input and output alphabets. It is shown that channel capacity is a lower semi-continuous function and that every block code with maximal probability of error /spl delta/ for a nominal channel for any /spl epsiv/>0 can be modified such that the modification has a probability of error less than /spl delta/+/spl epsiv/ for all channels in a sufficiently small neighborhood of the nominal channel.

The feedback capacity of additive stationary Gaussian noise channels is characterized as the solution to a variational problem. Toward this end, it is proved that the optimal feedback coding scheme is stationary. When specialized to the first-order autoregressive moving-average noise spectrum, this variational characterization yields a closed-form expression for the feedback capacity. In particular, this result shows that the celebrated Schalkwijk-Kailath coding scheme achieves the feedback capacity for the first-order autoregressive moving-average Gaussian channel, positively answering a long-standing open problem studied by Butman, Schalkwijk-Tiernan, Wolfowitz, Ozarow, Ordentlich, Yang-Kavcic-Tatikonda, and others. More generally, it is shown that a k-dimensional extension of the Schalkwijk-Kailath coding scheme achieves the feedback capacity for any autoregressive moving-average noise spectrum of order k. Simply put, the optimal transmitter iteratively refines the receiver's knowledge of the intended message

In this paper we analyze and design a Heterogenous cellular networks (HetNets) where base stations (BSs) are equipped with multi-antennas, serving a number of singleantenna user equipments (UEs) in downlink. We focus of space division multiple access (SDMA) whereby (i) zero-forcing beamforming vectors at the BSs are chosen based on the quantized channel direction information (CDI) and (ii) scheduled data rates are specified adaptively based on the quantized channel quality information (CQI). Adopting tools of stochastic geometry, we firstly, provide a tight approximation of the coverage performance of quantized SDMA beamforming in a closed-form that encompasses impacts of feedback capacity, density of BSs, and SIR thresholds under max-SIR cell association rule. Assuming CQI of each UE is its experienced SIR, we then exploit our analysis to devise a proper optimization problem to adaptively share feedback capacity between tiers, and also between CDI and CQI feedback. We do so by introducing net spatial throughput (NST) as the main performance metric, which is defined as the spatial throughput minus uplink penalty of feedback capacity per area per frame. Our numerical results show that serving more UEs calls for higher capacity of feedback channel without delivering strong NST. We further observe that one way to coup with such a weak performance is to densify the network in tier 2 wherever path-loss exponent is adequately large, e.g., installing many femto-cells in indoor.

Many industrial systems exhibit the nonlinear characteristics. Generally, the structure of the system is taken by feedback closed-loop for the purpose of realising the automatic control of industrial processes. Therefore, the industrial systems are the closed-loop feedback nonlinear systems which have complicated structures. The mathematical models of systems provide the support and basis for the design of the control system and the better control performance. However, it is hard to determine the models of closed-loop feedback nonlinear systems due to the complex structures. The goal of this study is to develop an identification way for a feedback nonlinear system including a forward channel and a feedback channel, where the forward channel is described by a controlled autoregressive model and the feedback channel takes the form of a static nonlinear function. By taking advantage of the least squares optimisation, a recursive least squares algorithm is established and shows its good performance to solve the identification problem for the feedback nonlinear system.