Feedback Channel Capacity Research Articles

Some New Results on the Gaussian Wiretap Feedback Channel

In this paper, the Gaussian wiretap feedback channel is revisited, and some new results on its secrecy capacity are obtained. To be specific, first, we show that the Schalkwijk–Kailath (SK) feedback scheme, which achieves the secrecy capacity of the degraded Gaussian wiretap feedback channel, also achieves the secrecy capacity of the non-degraded Gaussian wiretap feedback channel. Second, applying the existing secret key-based feedback schemes to Gaussian wiretap feedback channels, we derive some new lower bounds on the secrecy capacities of these models. Finally, we compare the performances of the above feedback schemes in the degraded and non-degraded Gaussian wiretap feedback channels and show which feedback scheme performs better for these channel models.

Capacity of Burst Noise-Erasure Channels With and Without Feedback and Input Cost

A class of burst noise-erasure channels which incorporate both errors and erasures during transmission is studied. The channel, whose output is explicitly expressed in terms of its input and a stationary ergodic noise-erasure process, is shown to have a so-called “quasi-symmetry” property under certain invertibility conditions. As a result, it is proved that a uniformly distributed input process maximizes the channel’s block mutual information, resulting in a closed-form formula for its non-feedback capacity in terms of the noise-erasure entropy rate and the entropy rate of an auxiliary erasure process. The feedback channel capacity is also characterized, showing that the feedback does not increase capacity and generalizing prior related results. The capacity-cost function of the channel with and without feedback is next investigated. A sequence of finite-letter upper bounds for the capacity-cost function without feedback is derived. Finite-letter lower bonds for the capacity-cost function with feedback are obtained using a specific encoding rule. Based on these bounds, it is demonstrated both numerically and analytically that feedback can increase the capacity-cost function for a class of channels with Markov noise-erasure processes.

Resource allocation for physical-layer security in OFDMAdownlinkwith imperfect CSI

We investigate the problem of resource allocation in a downlink orthogonal frequency-division multiple access (OFDMA) broadband network with an eavesdropper under the condition that both legitimate users and the eavesdropper are with imperfect channel state information (CSI). We consider three kinds of imperfect CSI: (1) noise and channel estimation errors, (2) feedback delay and channel prediction, and (3) limited feedback channel capacity, where quantized CSI is studied using rate-distortion theory because it can be used to establish an informationtheoretic lower bound on the capacity of the feedback channel. The problem is formulated as joint power and subcarrier allocation to optimize the maximum-minimum (max-min) fairness criterion over the users’ secrecy rate. The problem considered is a mixed integer nonlinear programming problem. To reduce the complexity, we propose a two-step suboptimal algorithm that separately performs power and subcarrier allocation. For a given subcarrier assignment, optimal power allocation is achieved by developing an algorithm of polynomial computational complexity. Numerical results show that our proposed algorithm can approximate the optimal solution.

Spatial Channel Estimation-Based FDD-MIMO Interference Alignment Systems

The practical feasibility of interference alignment (IA) is a major challenge in real-world implementation. The majority of the research contributions assume ideal channel reciprocity, which may be valid in time division duplex systems. In frequency division duplex (FDD) systems, large codebooks are utilized for channel quantization, and consume the feedback channel capacity. In this letter, a spatial channel estimation method is proposed for FDD-MIMO IA systems. The method utilizes the path correlation between the forward and reverse channels, where channels are on different frequency bands. A transformation matrix is employed to estimate the angles of departure of the forward channel. The proposed method shows a significant improvement of the sum rate without the need of feedback overhead bits.

Robust Joint Congestion Control and Scheduling for Time-Varying Multi-Hop Wireless Networks With Feedback Delay

Joint congestion control and link scheduling has been proposed as an approach to fair resource allocation in wireless networks. Existing solutions usually favor a distributed cross-layer deployment that requires timely communications among network components in seeking system stability and global optimum. However, this is unrealistic with feedback delay and channel capacity perturbation. The stability and efficiency of these algorithms face significant challenges. In this paper, we present a robust joint congestion control and scheduling algorithm, i.e., ROCS, for time-varying multi-hop mesh wireless networks with feedback delay, to bridge the gap between the existing approaches and the reality of wireless networks. The fundamental idea behind ROCS is capacity space projection, which combines the slow time scale part of the channel capacity and a margin estimated from the fast time scale part, to form a new capacity space. The resource allocation problem is formulated into a utility maximization framework over the newly generated capacity space. The problem is solved by a control algorithm consisting of link scheduling and congestion control. Link scheduling coordinates wireless link utilization, and congestion control allocates flow rates according to feedback information. Experiments conducted over simulated and real-world traces demonstrate that ROCS substantially achieves robustness and efficiency.

On the optimum signal constellation design for high-speed optical transport networks

In this paper, we first describe an optimum signal constellation design algorithm, which is optimum in MMSE-sense, called MMSE-OSCD, for channel capacity achieving source distribution. Secondly, we introduce a feedback channel capacity inspired optimum signal constellation design (FCC-OSCD) to further improve the performance of MMSE-OSCD, inspired by the fact that feedback channel capacity is higher than that of systems without feedback. The constellations obtained by FCC-OSCD are, however, OSNR dependent. The optimization is jointly performed together with regular quasi-cyclic low-density parity-check (LDPC) code design. Such obtained coded-modulation scheme, in combination with polarization-multiplexing, is suitable as both 400 Gb/s and multi-Tb/s optical transport enabling technology. Using large girth LDPC code, we demonstrate by Monte Carlo simulations that a 32-ary signal constellation, obtained by FCC-OSCD, outperforms previously proposed optimized 32-ary CIPQ signal constellation by 0.8 dB at BER of 10(-7). On the other hand, the LDPC-coded 16-ary FCC-OSCD outperforms 16-QAM by 1.15 dB at the same BER.

Downlink Throughput Maximization for OFDMA Systems With Feedback Channel Capacity Constraints

In this correspondence, we study the downlink throughput maximization for orthogonal frequency-division multiple-access (OFDMA) systems in the presence of feedback channel capacity constraints. We establish an information-theoretic lower bound on the capacity of feedback channel and build the corresponding test channel that achieves this lower bound. Based on the derived test channel, we formulate two optimization problems that maximize the downlink throughput with quantized channel state information (CSI): i) one problem where throughput is defined with the ergodic throughput and ii) the other problem with the outage throughput, from which we can see the performance limit for given limit feedback channels. We solve the throughput maximization problem through an iterative approach, which achieves the optimal ergodic throughput and the near-optimal outage throughput. Numerical results show that the downlink throughput with a limited feedback of CSI can be close to that with perfect CSI by exploiting correlation properties of downlink CSI for quantization.

Techniques of Transmitting Beamforming to Control the Generated Weights

In this paper, we consider the limited feedback Transmitting Beamforming for MISO systems. In conventional techniques, all vectors of a large codebook (CB), used for the feedback of the quantized channel state information (CSI), are broadcasted to all users, in a guard period which is followed by data burst periods. Instead of transmitting a high number of codevectors, we thought to divide the CB into several sub-codebooks (SC) and the broadcast would be based on the switch between them. Accordingly, a good performance can be provided while minimizing the required feedback channel capacity applying some proposed techniques such as “the switched Sub Codebook (SSC)” and “the Fairness SSC (FSSC)”. To minimize the quantization error, we propose two other techniques. The first is based on making Transmit SSC vectors controlled by a rotation weight (RW) to obtain almost a zero correlation between the SSC vectors used for the selected spatial channels. The second is based on introducing “the Schmidt algorithm” to construct an orthonormal weights using the generated weights. These two proposed techniques increase the probability of the selection of the worst case user on his best codevector to make zero the angle between his couple codevector and channel response. To analyze and validate the performance of these proposed techniques, simulation results are presented.

Robust and efficient quantization and coding for control of multidimensional linear systems under data rate constraints

AbstractRecently, we reported results on coding strategies for scalar feedback systems with data‐rate‐limited feedback channels in which the data‐rate constraints are time varying. Such rate‐varying channels are typically encountered in communication networks in which links between nodes are subject to noise, congestion, and intermittent disruption.The present paper describes results of extending this research into the multidimensional domain. An important consideration is that for systems of dimension greater than one, many classical feedback designs cannot be realized for operation near the theoretical minimum possible data rate. A novel control coding scheme will be presented, and in terms of this, it will be shown that the advantages of coarse signal quantization that had been reported earlier for scalar systems remain in the multidimensional case. The key is to allocate the communication bandwidth efficiently among faster and slower modes. We discuss various strategies that allocate bandwidth by scheduling the time slots assigned to each mode. In particular, we propose a ‘robust attention varying’ technique, whose merit will be discussed in terms of its robustness with respect to time‐varying communication channel capacity and also in terms of how well it operates when the feedback channel capacity is near the theoretical minimum data rate. Copyright © 2006 John Wiley & Sons, Ltd.

Optimal space-time scheduling for block fading channels with partial power feedbacks

The multi-user multiple-input-multiple-output (MIMO) space-time scheduling problem is the prime focus of the paper. Using multiple transmit (n T ) and receive antennas (n R ), it is well known that the link-level throughput will be increased linearly with respect to min[n T , n R ] without increasing the bandwidth and power budget. However, optimizing the link-level performance of the MIMO system does not always imply achieving scheduling-level optimization. Therefore, the design optimization across the link layer and the scheduling layer is very important to fully exploit the temporal and spatial dimensions of the communication channel. In this paper, we address the design of the optimal space-time scheduler for the multi-user MIMO system based on an information theoretical approach. Since full knowledge of channel matrix at the transmitter requires a feedback channel capacity not scalable with respect to n T (number of transmit antennas at mobiles) and n R (number of receive antennas at base station), we will assume two partial feedback models.

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions.

Variable rate multitone system for multipath fadingchannels

A continuous adaptive modulation multitone system for multipath fading channels is shown. To obtain a target BER and maximum aggregated rate. Each subcarrier bit rate is modified independently to adjust the transmitted signal to the spectral channel shape and to track the channel variations dynamically. Spectral efficiency and the required feedback channel capacity are obtained through simulation over a multipath Rician channel.

Strong converse, feedback channel capacity and hypothesis testing

Abstract 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.

Feedback communication using orthogonal signals

We consider a feedback communication system in which the forward and feedback channels are disturbed by additive noise and constrained in average power. Two block coding schemes are proposed in which the signals are orthogonal waveforms. A finite number of forward and feedback transmissions per message is made. Information received over the feedback channel is used to reduce the expected value of forward signal energy on all iterations after the first. Similarly, the expected value of feedback signal energy is reduced on all iterations after the first. These schemes, which are modifications of a feedback coding scheme due to Kramer, obtain improved error performance over one-way coding at all rates up to the forward channel capacity, provided only that the feedback channel capacity is greater than the forward channel capacity. They require less feedback power than existing feedback coding schemes to achieve a given error performance.