Panagiotis Botsinis

Quantum Search Algorithms, Quantum Wireless, and a Low-Complexity Maximum Likelihood Iterative Quantum Multi-User Detector Design

The high complexity of numerous optimal classic communication schemes, such as the maximum likelihood (ML) multiuser detector (MUD), often prevents their practical implementation. In this paper, we present an extensive review and tutorial on quantum search algorithms (QSA) and their potential applications, and we employ a QSA that finds the minimum of a function in order to perform optimal hard MUD with a quadratic reduction in the computational complexity when compared to that of the ML MUD. Furthermore, we follow a quantum approach to achieve the same performance as the optimal soft-input soft-output classic detectors by replacing them with a quantum algorithm, which estimates the weighted sum of a functions evaluations. We propose a soft-input soft-output quantum-assisted MUD (QMUD) scheme, which is the quantum-domain equivalent of the ML MUD. We then demonstrate its application using the design example of a direct-sequence code division multiple access system employing bit-interleaved coded modulation relying on iterative decoding, and compare it with the optimal ML MUD in terms of its performance and complexity. Both our extrinsic information transfer charts and bit error ratio curves show that the performance of the proposed QMUD and that of the optimal classic MUD are equivalent, but the QMUDs computational complexity is significantly lower.

Fixed-Complexity Quantum-Assisted Multi-User Detection for CDMA and SDMA

In a system supporting numerous users the complexity of the optimal Maximum Likelihood Multi-User Detector (ML MUD) becomes excessive. Based on the superimposed constellations of K users, the ML MUD outputs the specific multi-level K-user symbol that minimizes the Euclidean distance with respect to the faded and noise-contaminated received multi-level symbol. Explicitly, the Euclidean distance is considered as the Cost Function (CF). In a system supporting K users employing M-ary modulation, the ML MUD uses M^K CF evaluations (CFE) per time slot. In this contribution we propose an Early Stopping-aided Durr-H\o yer algorithm-based Quantum-assisted MUD (ES-DHA QMUD) based on two techniques for achieving optimal ML detection at a low complexity. Our solution is also capable of flexibly adjusting the QMUDs performance and complexity trade-off, depending on the computing power available at the base station. We conclude by proposing a general design methodology for the ES-DHA QMUD in the context of both CDMA and SDMA systems.

Quantum-Assisted Routing Optimization for Self-Organizing Networks

Self-organizing networks act autonomously for the sake of achieving the best possible performance. The attainable routing depends on a delicate balance of diverse and often conflicting quality-of-service requirements. Finding the optimal solution typically becomes an nonolynomial-hard problem, as the network size increases in terms of the number of nodes. Moreover, the employment of user-defined utility functions for the aggregation of the different objective functions often leads to suboptimal solutions. On the other hand, Pareto optimality is capable of amalgamating the different design objectives by providing an element of elitism. Although there is a plethora of bioinspired algorithms that attempt to address this optimization problem, they often fail to generate all the points constituting the optimal Pareto front. As a remedy, we propose an optimal multiobjective quantum-assisted algorithm, namely the nondominated quantum optimization algorithm (NDQO), which evaluates the legitimate routes using the concept of Pareto optimality at a reduced complexity. We then compare the performance of the NDQO algorithm to the state-of-the-art evolutionary algorithms, demonstrating that the NDQO algorithm achieves a near-optimal performance. Furthermore, we analytically derive the upper and lower bounds of the NDQO algorithmic complexity, which is of the order of O(N) and O(N√(N)) in the best and worst case scenario, respectively. This corresponds to a substantial complexity reduction of the NDQO from the order of O(N2) imposed by the brute-force method.

Low-Complexity Soft-Output Quantum-Assisted Multiuser Detection for Direct-Sequence Spreading and Slow Subcarrier-Hopping Aided SDMA-OFDM Systems

Low-complexity suboptimal multiuser detectors (MUDs) are widely used in multiple access communication systems for separating users, since the computational complexity of the maximum likelihood (ML) detector is potentially excessive for practical implementation. Quantum computing may be invoked in the detection procedure, by exploiting its inherent parallelism for approaching the ML MUDs performance at a substantially reduced number of cost function evaluations. In this contribution, we propose a soft-output (SO) quantum-assisted MUD achieving a near-ML performance and compare it to the corresponding SO ant colony optimization MUD. We investigate rank deficient direct-sequence spreading (DSS) and slow subcarrier-hopping aided (SSCH) spatial division multiple access orthogonal frequency division multiplexing systems, where the number of users to be detected is higher than the number of receive antenna elements used. We show that for a given complexity budget, the proposed SO-Dürr-Høyer algorithm (DHA) QMUD achieves a better performance. We also propose an adaptive hybrid SO-ML/SO-DHA MUD, which adapts itself to the number of users equipped with the same spreading sequence and transmitting on the same subcarrier. Finally, we propose a DSS-based uniform SSCH scheme, which improves the systems performance by 0.5 dB at a BER of 10-5, despite reducing the complexity required by the MUDs employed.

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful quantum error correction codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper, we provide an extensive step-by-step tutorial for designing extrinsic information transfer (EXIT) chart-aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed quantum irregular convolutional code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit.

Iterative Quantum-Assisted Multi-User Detection for Multi-Carrier Interleave Division Multiple Access Systems

With the proliferation of smart-phones and tablet PCs, the data rates of wireless communications have been soaring. Hence, the need for power-efficient communications relying on low-complexity multiple-stream detectors has become more pressing than ever. As a remedy, in this paper we design low-complexity soft-input soft-output quantum-assisted multi-user detectors (QMUD), which may be conveniently incorporated into state-of-the-art iterative receivers. Our design relies on extrinsic information transfer charts. Our QMUDs are then employed in multi-carrier interleave-division multiple-access (MC-IDMA) systems, which are investigated in the context of different channel code rate and spreading factor pairs, whilst fixing the total bandwidth requirement. One of our QMUDs is found to operate within 0.5 dB of the classical maximum a posteriori probability MUD after three iterations between the MUD and the decoders, while requiring only half its complexity, at a BER of 10-5 in the uplink of a rank-deficient MC-IDMA system relying on realistic imperfect channel estimation at the receiver, while supporting 14 users transmitting QPSK symbols.

Non-Dominated Quantum Iterative Routing Optimization for Wireless Multihop Networks

Routing in wireless multihop networks (WMHNs) relies on a delicate balance of diverse and often conflicting parameters, when aiming for maximizing the WMHN performance. Classified as a non-deterministic polynomial-time hard problem, routing in WMHNs requires sophisticated methods. As a benefit of observing numerous variables in parallel, quantum computing offers a promising range of algorithms for complexity reduction by exploiting the principle of quantum parallelism (QP), while achieving the optimum full-search-based performance. In fact, the so-called non-dominated quantum optimization (NDQO) algorithm has been proposed for addressing the multiobjective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of O(N) and O(N√N) in the best and worst case scenarios, respectively. However, as the number of nodes in the WMHN increases, the total number of routes increases exponentially, making its employment infeasible despite the complexity reduction offered. Therefore, we propose a novel optimal quantum-assisted algorithm, namely, the non-dominated quantum iterative optimization (NDQIO) algorithm, which exploits the synergy between the hardware and the QP for the sake of achieving a further complexity reduction, which is on the order of O(√N) and O(N√N) in the best and worst case scenarios, respectively. In addition, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared with the near-optimal NDQO algorithm, while having the same order of power consumption.

Noncoherent Quantum Multiple Symbol Differential Detection for Wireless Systems

In large-dimensional wireless systems, such as cooperative multicell processing, millimeterwave, and massive multiple input multiple output systems, or cells having a high user density, such as airports, train stations, and metropolitan areas, sufficiently accurate estimation of all the channel gains is required for performing coherent detection. Therefore, they may impose an excessive complexity. As an attractive design alternative, differential modulation relying on noncoherent detection may be invoked for eliminating the requirement for channel estimation at the base station, although at the cost of some performance degradation. In this treatise, we propose low-complexity hard-input hard-output, hard-input soft-output, as well as soft-input soft-output quantum-assisted multiple symbol differential detectors (MSDDs) that perform equivalently to the optimal, but highly complex maximum a posteriori probability MSDDs in multiuser systems, where the users are separated both in the frequency domain and in the time domain. When using an MSDD, the detection of a users symbols is performed over windows of differentially modulated symbols; hence, they exhibit an increased complexity with respect to the conventional differential detector while simultaneously improving the performance of the system, especially at high Doppler frequencies.

Fifteen Years of Quantum LDPC Coding and Improved Decoding Strategies

The near-capacity performance of classical low-density parity check (LDPC) codes and their efficient iterative decoding makes quantum LDPC (QLPDC) codes a promising candidate for quantum error correction. In this paper, we present a comprehensive survey of QLDPC codes from the perspective of code design as well as in terms of their decoding algorithms. We also conceive a modified non-binary decoding algorithm for homogeneous Calderbank-Shor-Steane-type QLDPC codes, which is capable of alleviating the problems imposed by the unavoidable length-four cycles. Our modified decoder outperforms the state-of-the-art decoders in terms of their word error rate performance, despite imposing a reduced decoding complexity. Finally, we intricately amalgamate our modified decoder with the classic uniformly reweighted belief propagation for the sake of achieving an improved performance.

Quantum-Aided Multi-User Transmission in Non-Orthogonal Multiple Access Systems

With the research on implementing a universal quantum computer being under the technological spotlight, new possibilities appear for their employment in wireless communications systems for reducing their complexity and improving their performance. In this treatise, we consider the downlink of a rank-deficient, multi-user system and we propose the discrete-valued and continuous-valued quantum-assisted particle swarm optimization (PSO) algorithms for performing vector perturbation precoding, as well as for lowering the required transmission power at the base station (BS), while minimizing the expected average bit error ratio (BER) at the mobile terminals. We use the minimum BER criterion. We show that the novel quantum-assisted precoding methodology results in an enhanced BER performance, when compared with that of a classical methodology employing the PSO algorithm, while requiring the same computational complexity in the challenging rank-deficient scenarios, where the number of transmit antenna elements at the BS is lower than the number of users. Moreover, when there is limited channel state information feedback from the users to the BS, due to the necessary quantization of the channel states, the proposed quantum-assisted precoder outperforms the classical precoder.