Arbitrarily Varying and Compound Classical-Quantum Channels and a Note on Quantum Zero-Error Capacities

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.

The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. The study of zero-error capacities dates right back to Shannon and the early days of information theory. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel. We further strengthen this result to show that there exist pairs of channels, neither of which have any zero-error classical capacity (as before), yet for which access to one copy of the joint channel even allows far more delicate quantum information to be transmitted perfectly. This subsumes the first result, and also implies that the quantum zero-error capacity can be superactivated. But it is strictly stronger than either of these. Indeed, this is the strongest conceivable form of superactivation, and nothing similar is possible for standard Shannon capacities of quantum channels or for zero-error capacities of classical channels.

We determine the secrecy capacities of arbitrarily varying quantum channels (AVQCs). Both secrecy capacities with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. As an application of our result for secret message transmission over AVQCs, we determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon “superactivation” for secrecy capacities of arbitrarily varying quantum channels, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We give therewith an answer to the question “When is the secrecy capacity a continuous function of the system parameters?,” which has been listed as an open problem in quantum information problem page of the Institut für Theoretische Physik (ITP) Hannover. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs. Ahlswede et al. made in 2013 the conjecture that the entanglement generating capacity of an AVQC is equal to its entanglement generating capacity under shared randomness assisted quantum coding. We demonstrate that the validity of this conjecture implies that the entanglement generating capacity, the entanglement distillation capacity, and the strong subspace transmission capacity of an AVQC are continuous functions of the system parameters. Consequently, under the premise of this conjecture, the secrecy capacities of an AVQC differ significantly from the general quantum capacities.

The coding gain and coding advantage criteria commonly used to analyse space-time codes are revisited. These criteria are based on the approximation of the average pairwise error probability achievable over a Rician multiple antenna channel at high signal-to-noise ratios. Both criteria appear to be inaccurate for a moderate number of antennas, especially in the environments with limited diversity and Rayleigh fading. In these cases, the average error probability may differ substantially from the outage probability for practically considered outage rates. A closed form upper bound on the outage pairwise error probability is derived. This bound gives rise to an alternative measure of coding advantage and coding gain that depend on the outage rate.

We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for classical-quantum channels; however, the exponents in their bounds only coincide when the channel is classical. In this paper, we show that these two exponents admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. Second, we establish a sphere-packing bound for classical-quantum channels, which significantly improves Dalai's prefactor from the order of subexponential to polynomial. Furthermore, the gap between the obtained error exponent for constant composition codes and the best known classical random coding exponent vanishes in the order of $o(\log n / n)$, indicating our sphere-packing bound is almost exact in the high rate regime. Finally, for a special class of symmetric classical-quantum channels, we can completely characterize its optimal error probability without the constant composition code assumption. The main technical contributions are two converse Hoeffding bounds for quantum hypothesis testing and the saddle-point properties of error exponent functions.

This paper analyzes the performance of multicarrier index modulation (MCIM) with greedy detection (GD) in a dual hop, multiple decode and forward (DF) relay network. We propose a novel partial relay selection (PRS) technique combined with index modulation and its energy detection. For performance analysis, we derive novel closed form solutions for both the average pairwise error probability (PEP) and the average symbol error probability (SEP) at the relays and destination over Nakagami-m fading channels. Unlike the information theoretical works, with presence of positive detection error in the relays, the derived expressions provide a useful insight into the error performance of PRS based MCIM in a multiple DF relay network under various fading conditions. Also, we address the impacts of both relays and different rates of sub-carrier index activation.

In the conventional Vertical Bell Laboratory Layered Space-Time (V-BLAST) receiver with successive interference cancellation (SIC) decoding, the diversity order for the first detected symbol is the lowest, hence its error probability dominates the overall average error probability. In this thesis, a new SIC scheme was presented, called iterative post SIC (IP-SIC) that can increase the diversity order to a fixed desired value for all symbols, thereby significantly reduce the overall average error probability. The key to the technique is that after the interference from all substreams is subtracted from the received vector (the resulting vector will be referred to as the modified received vector), the detected symbol times its channel vector is added to the modified received vector one at a time and the symbol is detected again. Important features of the proposed approach are the increase in diversity order for those symbols detected earlier and the flexibility of balancing the increase in diversity order and the suppression of remaining interference. The latter feature can be used to further reduce the average error probability. The proposed technique is applied to the V-BLAST and space-time block coded V-BLAST system and its performance and computational complexity are analyzed.

The error probability at a node of a digital circuit exposed to thermal noise agitation is investigated and the minimal dissipation–reliability relation for practical electronic circuits is derived. The digital circuit is modeled by an inverter chain with ideal transfer characteristics, and the error probability due to spurious data transfer caused by the thermal noise fluctuation is evaluated as a function of the node switching energy. The maximal error probability at each node allowed by the reliability requirement of the total system leads us to the minimal node energy dissipated per logical switching, which amounts to around 12 eV in the future 1010 gate system operated at a 10 GHz clock rate with a 104 FIT level reliability. In view of the device size-scaling trend of large-scale integrated circuits, the minimal node energy is expected to be reached at a feature size of 10–20 nm.

In this paper, we analyze the performance of single relay selection cooperative wireless networks using decode-and-forward relaying. Under optimum relay selection, the expressions for asymptotic outage probability, average symbol error probability are derived over Nakagami-m fading channels. Then we improve the performance of the system through optimum power allocation based on asymptotic outage probability and asymptotic average symbol error probability. Our results are verified through comparison with Monte Carlo simulations.

Time synchronization is a critical and vital piece of infrastructure for any distributed system or sensor network design or real time simulation. Sensor network have many of the same requirements as traditional distributed systems. Distributed wireless sensor networks make extensive use of synchronized time stamps in swarm navigation. Our target is to investigate the time synchronization in the network agents and determine the parameters of individual clock elements of the network. Therefore this paper shows design of clock model, time stamp exchange principle and linear regression for clock time update. It is found from the real-time simulation that the mean of error Probability Distribution Function (PDF) is 20 ms with maximum error probability 2.2% for free running oscillator. The outlayers were removed, and the error was minimized by linear regression method.

The average symbol error probability(ASEP) is an important measure to evaluate the performance of different modulation techniques over fading channels. The phenomenon of both shadowing and slow fading in wireless communication system is generally characterized by log-normal probability distribution. Approximating log-normal integrals by constructing Taylor series expansion of second order, a simple tight closed-form approximation for ASEP over log-normal fading channel is derived. This expression facilitates the computation of average symbol error rate for a broader class of coherent digital modulation schemes. The efficiency of the expression is numerically examined and comparison of the results is carried out in relation to the existing approximate expressions.

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.

New infinite-series expressions are obtained for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) of dual-hop amplify-and-forward (AF) relaying systems operating over Rician fading channels and dissimilar dual-hop AF systems operating over mixed Nakagami- $m$ /Rician fading channels. Precise analytical solutions for outage probability, as well as precise single-integral solutions for the ergodic capacity and the average symbol error probability, are obtained. Simulation results are used to verify the solutions obtained. It is shown that the limiting slopes of the average symbol error probability curves and the outage probability curves are not affected by the Rician fading parameter in contrast to the case of Nakagami- $m$ fading links. For the case of mixed fading links, the exact performance metrics are compared to performance bounds in the literature. It is shown that the existing performance bounds are not tight for medium ranges of SNR. The effects of the Rician and Nakagami- $m$ fading parameters on the system performance are also studied. It is shown that, while increasing the Rician parameter results in a notable SNR gain, increasing the Nakagami- $m$ parameter results in a negligible improvement in the system performance.

We present a moments-based approach to the performance analysis of L-branch equal-gain combining and maximal-ratio combining receivers, operating in independent or correlated, not necessarily identically distributed, Weibull fading. For both equal-gain combining and maximal-ratio combining receivers the moments of the output signal-to-noise ratio are obtained in closed-form. An accurate approximate expression is derived for the moment-generating function of the output signal-to-noise ratio of the equal-gain combining receiver utilizing the Padé approximants theory, while a closed-form expression for the corresponding MGF of the maximal-ratio combining receiver, is obtained. Significant performance criteria, such as average output signal-to-noise ratio, amount of fading and spectral efficiency at the low power regime, are extracted in closed-forms, using the moments of the output signal-to-noise ratio for both independent and correlative fading. Moreover, using the well-known moment-generating function approach, the outage and the average symbol error probability for several coherent, non-coherent, binary, and multilevel modulation schemes, are studied. The average symbol error probability of dual-branch equal-gain combining and maximal-ratio combining receivers is also obtained when correlative fading is considered in the diversity input branches. The proposed mathematical analysis is illustrated by various numerical results and validated by computer simulations.

In this paper, we consider a binary decision fusion problem for a wireless sensor network, with flat Rayleigh fading, where the sensors make local binary decisions on the status of a common binary phenomenon. A training-based channel estimator is used at the fusion center (FC) to estimate the complex Gausssian fading coefficients characterizing the (direct) links between sensors and FC. This (estimated) channel state information is used, by proper thresholding, to censor the sensors. On the other hand, a locally optimal decision threshold is considered for binary quantization at the sensors. The average detection error probability at the FC, under the use of a majority logic fusion rule, is selected as a qualitative measure of system performance and is evaluated by simulation. The impact of the choice of the censoring threshold on the average detection error probability, under several values of channel estimation error, channel SNR, and sensor SNR, is studied.