arXiv subjects

Francisco A. Monteiro

Publications and source records attributed to Francisco A. Monteiro.

13 recordsLinked to original sources

arXiv2025

GPU-Accelerated Syndrome Decoding for Quantum LDPC Codes below the 63 $μ$s Latency Threshold

This paper presents a GPU-accelerated decoder for quantum low-density parity-check (QLDPC) codes that achieves sub-$63$ $μ$s latency, below the surface code decoder's real-time threshold demonstrated on Google's Willow quantum processor. While surface codes have demonstrated below-threshold performance, the encoding rates approach zero as code distances increase, posing challenges for scalability. Recently proposed QLDPC codes, such as those by Panteleev and Kalachev, offer constant-rate encoding and asymptotic goodness but introduce higher decoding complexity. To address such limitation, this work presents a parallelized belief propagation decoder leveraging syndrome information on commodity GPU hardware. Parallelism was exploited to maximize performance within the limits of target latency, allowing decoding latencies under $50$ $μ$s for [[$784$, $24$, $24$]] codes and as low as $23.3$ $μ$s for smaller codes, meeting the tight timing constraints of superconducting qubit cycles. These results show that real-time, scalable decoding of asymptotically good quantum codes is achievable using widely available commodity hardware, advancing the feasibility of fault-tolerant quantum computation beyond surface codes.

quant-ph↗

arXiv2024

Efficient entanglement purification based on noise guessing decoding

In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.

quant-ph↗

arXiv2024

Entanglement Routing Based on Fidelity Curves

How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between $1$ and $1.4$, depending on the network)

quant-ph↗

arXiv2024

Fault-tolerant noise guessing decoding of quantum random codes

This work addresses the open question of implementing fault-tolerant QRLCs with feasible computational overhead. We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. A first approach, introduced by Cruz et al., only considered channel errors, and perfect gates at the decoder. Here, we analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique, when considering preparation, measurement, and gate errors in the syndrome extraction procedure, while also accounting for error degeneracy. Our findings indicate a threshold error rate ($\pth$) of approximately $\pnum$ in the asymptotic limit, while considering realistic noise levels in the mentioned physical procedures.

quant-ph↗

arXiv2023

Quantum Error Correction via Noise Guessing Decoding

Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and present rigid code lengths and code rates. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime, for any chosen code length when the code rate is sufficiently high. A recently proposed strategy for decoding classical codes called GRAND (guessing random additive noise decoding) opened doors to efficiently decode classical random linear codes (RLCs) performing near the maximum rate of the finite blocklength regime. By using noise statistics, GRAND is a noise-centric efficient universal decoder for classical codes, provided that a simple code membership test exists. These conditions are particularly suitable for quantum systems, and therefore the paper extends these concepts to quantum random linear codes (QRLCs), which were known to be possible to construct but whose decoding was not yet feasible. By combining QRLCs and a newly proposed quantum-GRAND, this work shows that it is possible to decode QECCs that are easy to adapt to changing conditions. The paper starts by assessing the minimum number of gates in the coding circuit needed to reach the QRLCs' asymptotic performance, and subsequently proposes a quantum-GRAND algorithm that makes use of quantum noise statistics, not only to build an adaptive code membership test, but also to efficiently implement syndrome decoding.

quant-ph↗

arXiv2023

Symbol-Level Noise-Guessing Decoding with Antenna Sorting for URLLC Massive MIMO

Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable latency. Only short codewords can eliminate the requirement for interleaving and reduce decoding latency. This paper suggests a coding and decoding method which, when combined with the high spectral efficiency of spatial multiplexing, can provide URLLC over a fading channel. Random linear coding and high-order modulation are used to transmit information over a massive multiple-input multiple-output (mMIMO) channel, followed by zero-forcing detection and guessing random additive noise decoding (GRAND) at a receiver. A variant of GRAND, called symbol-level GRAND, originally proposed for single-antenna systems that employ high-order modulation schemes, is generalized to spatial multiplexing. The paper studies the impact of the orthogonality defect of the underlying mMIMO lattice on symbol-level GRAND, and proposes to leverage side-information that comes from the mMIMO channel-state information and relates to the reliability of each receive antenna. This induces an antenna sorting step, which further reduces decoding complexity by over 80\% when compared to bit-level GRAND.

cs.IT↗

arXiv2023

URLLC with Coded Massive MIMO via Random Linear Codes and GRAND

A present challenge in wireless communications is the assurance of ultra-reliable and low-latency communication (URLLC). While the reliability aspect is well known to be improved by channel coding with long codewords, this usually implies using interleavers, which introduce undesirable delay. Using short codewords is a needed change to minimizing the decoding delay. This work proposes the combination of a coding and decoding scheme to be used along with spatial signal processing as a means to provide URLLC over a fading channel. The paper advocates the use of random linear codes (RLCs) over a massive MIMO (mMIMO) channel with standard zero-forcing detection and guessing random additive noise decoding (GRAND). The performance of several schemes is assessed over a mMIMO flat fading channel. The proposed scheme greatly outperforms the equivalent scheme using 5G's polar encoding and decoding for signal-to-noise ratios (SNR) of interest. While the complexity of the polar code is constant at all SNRs, using RLCs with GRAND achieves much faster decoding times for most of the SNR range, further reducing latency.

cs.IT↗

arXiv2023

Distributing Multipartite Entanglement over Noisy Quantum Networks

A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising simultaneously the final state fidelity and the rate of entanglement distribution. Furthermore, we determine the conditions yielding this simultaneous optimality for GHZ states with a higher number of qubits, and for other types of multipartite entanglement. Our algorithm is general also in the sense that it can optimise simultaneously arbitrary parameters. This work opens the way to optimally generate multipartite quantum correlations over noisy quantum networks, an important resource for distributed quantum technologies.

quant-ph↗

arXiv2022

Symbol-Level GRAND for High-Order Modulation over Flat Fading Channels

Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for ultra-reliable low-latency communications, as it supports high-rate error correction codes that generate short-length codewords. GRAND estimates transmitted codewords by guessing the error patterns that altered them during transmission. The guessing process requires the generation and testing of error patterns that are arranged in increasing order of Hamming weight. This approach is fitting for binary transmission over additive white Gaussian noise channels. This letter considers transmission of coded and modulated data over flat fading channels and proposes a variant of GRAND, which leverages information on the modulation scheme and the fading channel. In the core of the proposed variant, referred to as symbol-level GRAND, is an analytical expression that computes the probability of occurrence of an error pattern and determines the order with which error patterns are tested. Simulation results demonstrate that symbol-level GRAND produces estimates of the transmitted codewords notably faster than the original GRAND at the cost of a small increase in memory requirements.

cs.IT↗

arXiv2021

Massive Wireless Energy Transfer with Statistical CSI Beamforming

Wireless energy transfer (WET) is a promising solution to enable massive machine-type communications (mMTC) with low-complexity and low-powered wireless devices. Given the energy restrictions of the devices, instant channel state information at the transmitter (CSIT) is not expected to be available in practical WET-enabled mMTC. However, because it is common that the terminals appear spatially clustered, some degree of spatial correlation between their channels to the base station (BS) is expected to occur. The paper considers a massive antenna array at the BS for WET that only has access to i) the first and second order statistics of the Rician channel component of the multiple-input multiple-output (MIMO) channel and also to ii) the line-of-sight MIMO component. The optimal precoding scheme that maximizes the total energy available to the single-antenna devices is derived considering a continuous alphabet for the precoders, permitting any modulated or deterministic waveform. This may lead to some devices in the clusters being assigned a low fraction of the total available power in the cluster, creating a rather uneven situation among them. Consequently, a fairness criterion is introduced, imposing a minimum amount of power allocated to the terminals. A piece-wise linear harvesting circuit is considered at the terminals, with both saturation and a minimum sensitivity, and a constrained version of the precoder is also proposed by solving a non-linear programming problem. A paramount benefit of the constrained precoder is the encompassment of fairness in the power allocation to the different clusters. Moreover, given the polynomial complexity increase of the proposed unconstrained precoder, and the observed linear gain of the system's available sum-power with an increasing number of antennas at the ULA, the use of massive antenna arrays is desirable.

eess.SP↗

arXiv2020

A Low-Complexity Beamforming Design for Multiuser Wireless Energy Transfer

Wireless energy transfer (WET) is a green enabler of low-power Internet of Things (IoT). Therein, traditional optimization schemes relying on full channel state information (CSI) are often too costly to implement due to excessive energy consumption and high processing complexity. This letter proposes a simple, yet effective, energy beamforming scheme that allows a multi-antenna power beacon (PB) to fairly power a set of IoT devices by only relying on the first-order statistics of the channels. In addition to low complexity, the proposed scheme performs favorably as compared to benchmarking schemes and its performance improves as the number of PB's antennas increases. Finally, it is shown that further performance improvement can be achieved through proper angular rotations of the PB.

cs.IT↗

arXiv2015

Full-Duplex Relaying in MIMO-OFDM Frequency-Selective Channels with Optimal Adaptive Filtering

In-band full-duplex transmission allows a relay station to theoretically double its spectral efficiency by simultaneously receiving and transmitting in the same frequency band, when compared to the traditional half-duplex or out-of-band full-duplex counterpart. Consequently, the induced self-interference suffered by the relay may reach considerable power levels, which decreases the signal-to-interference-plus-noise ratio (SINR) in a decode-and-forward (DF) relay, leading to a degradation of the relay performance. This paper presents a technique to cope with the problem of self-interference in broadband multiple-input multiple-output (MIMO) relays. The proposed method uses a time-domain cancellation in a DF relay, where a replica of the interfering signal is created with the help of a recursive least squares (RLS) algorithm that estimates the interference frequency-selective channel. Its convergence mean time is shown to be negligible by simulation results, when compared to the length of a typical orthogonal-frequency division multiplexing (OFDM) sequences. Moreover, the bit-error-rate (BER) and the SINR in a OFDM transmission are evaluated, confirming that the proposed method extends significantly the range of self-interference power to which the relay is resilient to, when compared with other mitigation schemes.

cs.IT↗

arXiv2015

Massive MIMO Full-Duplex Relaying with Optimal Power Allocation for Independent Multipairs

With the help of an in-band full-duplex relay station, it is possible to simultaneously transmit and receive signals from multiple users. The performance of such system can be greatly increased when the relay station is equipped with a large number of antennas on both transmitter and receiver sides. In this paper, we exploit the use of massive arrays to effectively suppress the loopback interference (LI) of a decode-and-forward relay (DF) and evaluate the performance of the end-to-end (e2e) transmission. This paper assumes imperfect channel state information is available at the relay and designs a minimum mean-square error (MMSE) filter to mitigate the interference. Subsequently, we adopt zero-forcing (ZF) filters for both detection and beamforming. The performance of such system is evaluated in terms of bit error rate (BER) at both relay and destinations, and an optimal choice for the transmission power at the relay is shown. We then propose a complexity efficient optimal power allocation (OPA) algorithm that, using the channel statistics, computes the minimum power that satisfies the rate constraints of each pair. The results obtained via simulation show that when both MMSE filtering and OPA method are used, better values for the energy efficiency are attained.

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