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 multilevel 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 MK CF evaluations (CFE) per time slot. In this contribution we propose an Early Stopping-aided Durr-Høyer 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 QMUD's 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 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 function’s 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 QMUD’s computational complexity is significantly lower

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

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

Joint quantum-assisted channel estimation and data detection

Joint Channel Estimation (CE) and Multi-User Detection (MUD) has become a crucial part of iterative receivers. In this paper we propose a Quantum-assisted Repeated Weighted Boosting Search (QRWBS) algorithm for CE and we employ it in the uplink of MIMO-OFDM systems, in conjunction with the Maximum A posteriori Probability (MAP) MUD and a near-optimal Quantum-assisted MUD (QMUD). The performance of the QRWBS-aided CE is evaluated in rank-deficient systems, where the number of receive Antenna Elements (AE) at the Base Station (BS) is lower than the number of supported users. The effect of the Channel Impulse Response (CIR) prediction filters, of the Power Delay Profile (PDP) of the channels and of the Doppler frequency have on the attainable system performance is also quantified. The proposed QRWBS-aided CE is shown to outperform the RWBS-aided CE, despite requiring a lower complexity, in systems where iterations are invoked between the MUD, the CE and the channel decoders at the receiver. In a system, where U=7 users are supported with the aid of P=4 receive AEs, the joint QRWBS-aided CE and QMUD achieves a 2 dB gain, when compared to the joint RWBS-aided CE and MAP MUD, despite imposing 43% lower complexity

Quantum error correction protects quantum search algorithms against decoherence

When quantum computing becomes a wide-spread commercial reality, Quantum Search Algorithms (QSA) and especially Grover’s QSA will inevitably be one of their main applications, constituting their cornerstone. Most of the literature assumes that the quantum circuits are free from decoherence. Practically, decoherence will remain unavoidable as is the Gaussian noise of classic circuits imposed by the Brownian motion of electrons, hence it may have to be mitigated. In this contribution, we investigate the effect of quantum noise on the performance of QSAs, in terms of their success probability as a function of the database size to be searched, when decoherence is modelled by depolarizing channels’ deleterious effects imposed on the quantum gates. Moreover, we employ quantum error correction codes for limiting the effects of quantum noise and for correcting quantum flips. More specifically, we demonstrate that, when we search for a single solution in a database having 4096 entries using Grover’s QSA at an aggressive depolarizing probability of 10-3, the success probability of the search is 0.22 when no quantum coding is used, which is improved to 0.96 when Steane’s quantum error correction code is employed. Finally, apart from Steane’s code, the employment of Quantum Bose-Chaudhuri-Hocquenghem (QBCH) codes is also considered

Quantum-assisted multi-user wireless systems

The high complexity of numerous optimal classical communication schemes, such as the Maximum Likelihood (ML) and Maximum A posteriori Probability (MAP) Multi-User Detector (MUD) designed for coherent detection or the ML and MAP Multiple-Symbol Differential Detectors (MSDD) conceived for non-coherent receivers often prevents their practical implementation. In this thesis we commence with a review and tutorial on Quantum Search Algorithms (QSA) and propose a number of hard-output and iterative Quantum-assisted MUDs (QMUD) and MSDDs (QMSDD).We employ a QSA, termed as the Durr-Hyer Algorithm (DHA) that finds the minimum of a function in order to perform near-optimal detection with quadratic reduction in the computational complexity, when compared to that of the ML MUD / MSDD. Two further techniques conceived for reducing the complexity of the DHA-based Quantum-assisted MUD (QMUD) are also proposed. These novel QMUDs / QMSDDs are employed in the uplink of various multiple access systems, such as Direct Sequence Code Division Multiple Access systems, Space Division Multiple Access systems as well as in Direct-Sequence Spreading and Slow Subcarrier Hopping SDMA systems amalgamated with Orthogonal Frequency Division Multiplexing and Interleave Division Multiple Access systems.Furthermore, we follow a quantum approach to achieve the same performance as the optimal Soft Input Soft-Output (SISO) classical detectors by replacing them with a quantum algorithm, which estimates the weighted sum of all the evaluations of a function. We propose a SISO QMUD / QMSDD scheme, which is the quantum-domain equivalent of the MAP MUD / MSDD. Both our EXtrinsic Information Transfer (EXIT) charts and Bit Error Ratio (BER) curves show that the computational complexity of the proposed QMUD / QMSDD is significantly lower than that of the MAP MUD / MSDD, whilst their performance remains equivalent. Moreover, we propose two additional families of iterative DHA-based QMUD / QMSDDs for performing near-optimal MAP detection exhibiting an even lower tunable complexity than the QWSA QMUD. Several variations of the proposed QMUD / QMSDDs have been developed and they are shown to perform better than the state-of-the-art low-complexity MUDs / MSDDs at a given complexity. Their iterative decoding performance is investigated with the aid of non-Gaussian EXIT charts.<br/

Low-complexity soft-output quantum-assisted multi-user detection for direct-sequence spreading and slow subcarrier-hopping aided SDMA-OFDM systems

Low-complexity sub-optimal Multi-User Detectors (MUD) 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 MUD’s performance at a substantially reduced number of Cost Function (CF) 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 (ACO) MUD. We investigate rank deficient Direct-Sequence Spreading (DSS) and Slow Subcarrier-Hopping aided (SSCH) Spatial Division Multiple Access (SDMA) Orthogonal Frequency Division Multiplexing (OFDM) 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 SODHA 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 system’s performance by 0:5 dB at a BER of 105, despite reducing the complexity required by the MUDs employed