Achievable Error Probability Research Articles

A Multiobjective Optimization Approach to Obtain Decision Thresholds for Distributed Detection in Wireless Sensor Networks

For distributed detection in a wireless sensor network, sensors arrive at decisions about a specific event that are then sent to a central fusion center that makes global inference about the event. For such systems, the determination of the decision thresholds for local sensors is an essential task. In this paper, we study the distributed detection problem and evaluate the sensor thresholds by formulating and solving a multiobjective optimization problem, where the objectives are to minimize the probability of error and the total energy consumption of the network. The problem is investigated and solved for two types of fusion schemes: 1) parallel decision fusion and 2) serial decision fusion. The Pareto optimal solutions are obtained using two different multiobjective optimization techniques. The normal boundary intersection (NBI) method converts the multiobjective problem into a number of single objective-constrained subproblems, where each subproblem can be solved with appropriate optimization methods and nondominating sorting genetic algorithm-II (NSGA-II), which is a multiobjective evolutionary algorithm. In our simulations, NBI yielded better and evenly distributed Pareto optimal solutions in a shorter time as compared with NSGA-II. The simulation results show that, instead of only minimizing the probability of error, multiobjective optimization provides a number of design alternatives, which achieve significant energy savings at the cost of slightly increasing the best achievable decision error probability. The simulation results also show that the parallel fusion model achieves better error probability, but the serial fusion model is more efficient in terms of energy consumption.

Capacity and Random-Coding Exponents for Channel Coding With Side Information

Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels are considered: 1) compound discrete memoryless channels (CDMC), and 2) channels with arbitrary memory, subject to an additive cost constraint, or more generally, to a hard constraint on the conditional type of the channel output given the input. Both problems are closely connected. The random-coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder, which may be thought of as an empirical generalized maximum a posteriori decoder. For channels with arbitrary memory, the random-coding exponents are larger than their CDMC counterparts. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning

Classical and quantum fingerprinting with shared randomness and one-sided error

Within the simultaneous message passing model of communication complexity, under a public-coin assumption, we derive the minimum achievable worst-case error probability of a classical fingerprinting protocol with one-sided error. We then present entanglement-assisted quantum fingerprinting protocols attaining worst-case error probabilities that breach this bound.

Coding and Signal Space Diversity for a Class of Fading and Impulsive Noise Channels

The transmission over the Gaussian mixture noise channel with perfect channel state information at the receiver side is considered. Lower and upper bounds on the achievable pairwise error probability (PEP) are derived for finite and infinite codeword lengths. It is shown that diversity codes, i.e., unitary transforms, can be applied to achieve a diversity gain. A large class of diversity codes is determined for which-if the codeword length is increased-the PEP between any two codewords approaches either zero or the lower bound on the PEP.

Multiaccess Quantum Channels

Shared communication channels are subject to multiple-access interference. Transmitter and receiver design techniques that explicitly deal with this interference have been shown to improve substantially the performance of communication systems over radio-frequency and other "classical" channels. Quantum multiple-access communication channels, on the other hand, have received comparatively little attention. In this paper, an input-output model for multiple-access quantum channels relevant to optical communications is proposed. The model accounts for multiaccess interference, signal attenuation, and random noise, and can be used in the analysis and design of communication systems. Using a result from optimization, a perturbation method is developed to find the minimum achievable error probability in small-interference channels. It is shown that the quantum measurement that minimizes the error probability in a no-interference channel is robust in the presence of small multiaccess interference. The results are illustrated with numerical examples, which show that optimal quantum detectors can significantly outperform conventional detectors even for moderate levels of crosstalk.

Genetic algorithm assisted error probability optimisation for beamforming

A novel Genetic Algorithm (GA) assisted direct error probability optimisation technique is proposed for adaptive beamforming, which reduces the achievable error probability by nearly two orders of magnitude at a signal-to-noise ratio of 10dB in the investigated scenario in comparison to the minimum mean-squared error beamforming benchmarker.

Coder selection for lossy compression of still images

A criterion for selecting a lossy coder for still images is proposed. The “optimum” coder using the proposed criterion is selected to minimize the maximum Chernoff information between the distribution for the original and any distribution from the optimal achievable region. The resulting coder has the property that the best achievable probability of error over the problems of hypothesis testing between these distributions, is greater than the best Bayesian error probability for any other choice of coder. The coder selection procedure may be applied without a knowledge of what distortion measure is more suitable for images or a knowledge of the properties of the human visual perception. Several examples of coder selection are included to illustrate the procedure.

Analysis of the impact of channel estimation errors on the performance of a decision-feedback equalizer in fading multipath channels

A coherent receiver with a decision-feedback equalizer (DFE) operating on a Rayleigh fading channel under a suitable adaptive algorithm is considered. In the analysis of a DFE, a common assumption is that the receiver has perfect knowledge of the channel impulse response. However, this is not the case in practice, and for a rapidly fading channel, errors in channel tracking can become significant. We analyze theoretically the impact of these errors on the performance of a multichannel DFE. The expressions obtained for the achievable average MPSK bit error probabilities depend on the estimation error covariance. In order to specify this matrix, we focus on a special case when a Kalman filter is used as an optimal channel estimator. In this case, the probability of bit error can be assessed directly in terms of channel fading model parameters, the most interesting of which is the fading rate. Our results show the penalty imposed by imperfect channel estimation, as well as the fading-induced irreducible error rates. >

Joint detection with coherent receiver antenna diversity in CDMA mobile radio systems

In code division multiple access (CDMA) mobile radio systems, both intersymbol interference and multiple access interference arise which can be combated by using either elaborate optimum or favorable suboptimum joint detection (JD) techniques. Furthermore, the time variation of the radio channels leads to degradations of the receiver performance. These degradations can be reduced by applying diversity techniques. Using coherent receiver antenna diversity (CRAD) is especially attractive because only the signal processing at the receiver must be modified. In the present paper, the application of CRAD to the more critical uplink of CDMA mobile radio systems with suboptimum JD techniques is investigated for maximal-ratio combining. The authors study six different suboptimum JD techniques based on decorrelating matched filtering, Gauss-Markov estimation, and minimum mean square error estimation with and without decision feedback. These six suboptimum JD techniques which are well-known for single antenna receivers are extended for the application to CRAD. A main concern of the paper is the determining of the SNR performance of the presented JD techniques for CRAD and the achievable average uncoded bit error probabilities for the transmission over rural area, typical urban and bad urban mobile radio channels are determined.

Achievable performance over the correlated Rician channel

The correlated Rician channel is a useful model for a slowly fading channel, in which the complex fading process is composed of two quadrature Gaussian processes with a given autocorrelation function. For slow fading the correlation between adjacent symbols is relatively high. The authors investigate the achievable error probabilities over the channel, employing coherent detection and ideal side information on the realization of the fading processes at the receiver. An underlying decoding delay constraint which precludes the use of (ideal) interleaving is assumed. Coded BPSK performance is addressed both with and without the piecewise constant approximation (according to which the fading value remains constant during the symbol duration). For the latter case, that is no piecewise constant approximation, the analysis relies on the Fredholm determinant associated with the fading process autocorrelation function. The authors focus on the exponentially correlated channel. The "worst case" pairs of codewords are identified. The exponential behavior of the error probability with random coding (and i.i.d. Gaussian inputs) is analyzed, and the behavior of the cut-off rate and capacity is addressed. The results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block-fading channel model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An application of rate-distortion theory to a converse to the coding theorem

A lower bound to the information rate R(D) for a discrete memoryless source with a fidelity criterion is presented for the case in which the distortion matrix contains the same set of entries, perhaps permuted, in each column. A necessary and sufficient condition for R(D) to equal this bound is given. In particular, if the smallest column element is zero and occurs once in each row, then there is a range of D, 0 \leq D \leq D_{1} , in which equality holds. These results are then applied to the special case of d_{ij}= 1 - \delta_{ij} , for which the average distortion is just the probability of incorrectly reproducing the source output. We show how to construct R(D) for this case, from which one can solve for the minimum achievable probability of error when transmitting over a channel of known capacity.

A per letter converse to the channel coding theorem

By relating the average probability of error to the distortion measure of a source-sink pair, we prove a converse to the channel coding theorem. This converse lower-bounds the probability of error per source letter. It differs from the more familiar "weak" and "strong" converses which bound the probability of error of an entire message. The result is applicable to all stationary sources, all channels, and all block lengths. Lower-bounding the rate distortion function of the source-sink pair with which the channel is to be used reduces the new result to a lower bound on the achievable probability of error per source letter expressed in terms of the source entropy, alphabet size, and maximum achievable average mutual information on the channel. This latter result had been proved previously only for a memoryless channel operating with an independent letter source.