Zunaira Babar

Entanglement-Assisted Quantum Turbo Codes

An unexpected breakdown in the existing theory of quantum serial turbo coding is that a quantum convolutional encoder cannot simultaneously be recursive and non-catastrophic. These properties are essential for quantum turbo code families to have a minimum distance growing with blocklength and for their iterative decoding algorithm to converge, respectively. Here, we show that the entanglement-assisted paradigm simplifies the theory of quantum turbo codes, in the sense that an entanglement-assisted quantum (EAQ) convolutional encoder can possess both of the aforementioned desirable properties. We give several examples of EAQ convolutional encoders that are both recursive and non-catastrophic and detail their relevant parameters. We then modify the quantum turbo decoding algorithm of Poulin , in order to have the constituent decoders pass along only extrinsic information to each other rather than a posteriori probabilities as in the decoder of Poulin , and this leads to a significant improvement in the performance of unassisted quantum turbo codes. Other simulation results indicate that entanglement-assisted turbo codes can operate reliably in a noise regime 4.73 dB beyond that of standard quantum turbo codes, when used on a memoryless depolarizing channel. Furthermore, several of our quantum turbo codes are within 1 dB or less of their hashing limits, so that the performance of quantum turbo codes is now on par with that of classical turbo codes. Finally, we prove that entanglement is the resource that enables a convolutional encoder to be both non-catastrophic and recursive because an encoder acting on only information qubits, classical bits, gauge qubits, and ancilla qubits cannot simultaneously satisfy them.

EXIT-Chart-Aided Near-Capacity Quantum Turbo Code Design

High detection complexity is the main impediment in future gigabit-wireless systems. However, a quantum-based detector is capable of simultaneously detecting hundreds of user signals by virtue of its inherent parallel nature. This, in turn, requires near-capacity quantum error correction codes for protecting the constituent qubits of the quantum detector against undesirable environmental decoherence. In this quest, we appropriately adapt the conventional nonbinary EXtrinsic Information Transfer (EXIT) charts for quantum turbo codes (QTCs) by exploiting the intrinsic quantum-to-classical isomorphism. The EXIT chart analysis not only allows us to dispense with the time-consuming Monte Carlo simulations but facilitates the design of near-capacity codes without resorting to the analysis of their distance spectra as well. We have demonstrated that our EXIT chart predictions are in line with the Monte Carlo simulation results. We have also optimized the entanglement-assisted QTC using EXIT charts, which outperforms the existing distance-spectra-based QTCs. More explicitly, the performance of our optimized QTC is as close as 0.3 dB to the corresponding hashing bound.

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.

Near-Capacity Code Design for Entanglement-Assisted Classical Communication over Quantum Depolarizing Channels

We have conceived a near-capacity code design for entanglement-assisted classical communication over the quantum depolarizing channel. The proposed system relies on efficient near-capacity classical code designs for approaching the entanglement-assisted classical capacity of a quantum depolarizing channel. It incorporates an Irregular Convolutional Code (IRCC), a Unity Rate Code (URC) and a soft-decision aided Superdense Code (SD), which is hence referred to as an IRCC-URC-SD arrangement. Furthermore, the entanglement-assisted classical capacity of an N-qubit superdense code transmitted over a depolarizing channel is invoked for benchmarking. It is demonstrated that the proposed system operates within 0.4 dB of the achievable noise limit for both 2-qubit as well as 3-qubit SD schemes. More specifically, our design exhibits a deviation of only 0.062 and 0.031 classical bits per channel use from the corresponding 2-qubit and 3-qubit capacity limits, respectively. The proposed system is also benchmarked against the classical convolutional and turbo codes.

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.

Reduced-Complexity Syndrome-Based TTCM Decoding

The iterative decoder of Turbo Trellis Coded Modulation (TTCM) exchanges extrinsic information between the constituent TCM decoders, which imposes a high computational complexity at the receiver. Therefore we conceive the syndrome-based block decoding of TTCM, which is capable of reducing the decoding complexity by disabling the decoder, when syndrome becomes zero. Quantitatively, we demonstrate that a decoding complexity reduction of at least 17% is attained at high SNRs, with at least 20% and 45% reduction in the 5^{th} and 6^{th} iterations, respectively.

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.