Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant (FT) implementations. In this paper, we investigate the performance of QEC schemes taking into account that quantum gates and measurements are themselves error-prone. We derive bounds for the failure probability of Shor-style FT-QEC schemes using limited structural information, such as the number of flag qubits and quantum gates. Our analysis separates and quantifies two key contributors to the failure rate: decoding errors and residual errors arising from circuit-level faults. The derived bounds highlight fundamental limitations in Shor-style FT-QEC performance and quantify how circuit imperfections degrade error correction capabilities, under the assumption of depolarizing noise.

Reliable quantum computation requires fault-tolerant protocols to prevent errors from propagating during syndrome extraction in quantum error correction. We present a novel fault-tolerant syndrome extraction technique for CSS codes, which we refer to as the cut-cat state scheme. While each ancilla qubit interacts non-fault-tolerantly with a pair of data qubits, we introduce additional cat stabilizer measurements to identify and correct the resulting hook errors. Our approach maintains the key benefit of cat-based extraction, i.e., parallelized data qubit interactions, while reducing the number of simultaneous qubits required by more than half. Compared to flag-based state-of-the-art protocols, the cut-cat scheme offers a notable advantage in terms of two-qubit gate count as the code distance increases.

Quantum computers are highly vulnerable to noise, necessitating the use of error-correcting codes to protect stored data. Errors must be continuously corrected over time to counteract decoherence using appropriate decoders. Therefore, fast decoding strategies capable of handling real-time syndrome extraction are crucial for achieving fault-tolerant quantum computing. In this paper, we introduce the bubble clustering (BC) decoder for quantum surface codes, which serves as a low-latency replacement for MWPM, achieving significantly faster execution at the cost of a slight performance degradation. This speed boost is obtained leveraging an efficient cluster generation based on bubbles centered on defects, and avoiding the computational overhead associated with cluster growth and merging phases, commonly adopted in traditional decoders. Our complexity analysis reveals that the proposed decoder operates with a complexity on the order of the square of the number of defects. For moderate physical error rates, this is equivalent to linear complexity in the number of data qubits.

We introduce a massive multiple access scheme designed to meet different trade-offs between reliability, scalability, and latency. To maximize the number of successfully decoded users, the scheme builds upon coded random access, incorporating both grant-free and grant-based procedures, along with a massive acknowledgment phase conducted at the base station. The main design premise is the establishment of two distinct latency deadlines: the first one guaranteeing high reliability (e.g., between 99% and 99.99%), and the second one enforcing ultra-high reliability, even above 99.9999%. This dual-latency approach, supplemented with massive MIMO, enables the system to support a higher number of active users per frame while meeting stringent reliability requirements. Throughout the paper, we present a theoretical analysis and derive performance bounds to guide and support effective system design. The approach opens the door for the development of critical services that bridge the gap between massive machine-type communication (mMTC) and ultra-reliable and low-latency communication (URLLC), providing a more flexible and efficient framework for next-generation systems.

In this paper, feedback-aided coded random access (CRA) protocols for grant-free massive access, with and without exploitation of the power domain, are investigated. The developed schemes can support non-instantaneous acknowledgment messages, along with their time resources, with very little penalty in terms of the achieved tradeoff between scalability, reliability, and latency. The new CRA-type protocols rely on waiting slots introduced between consecutive transmissions from the same device to pipeline the feedback reception without degrading the throughput. Their performance can be further enhanced by exploitation of the power domain, in particular by introduction of a deterministic power selection scheme designed for transmission of different packet replicas over a short time window. The system performance is investigated assuming a realistic wireless channel model, a massive MIMO base station, and a realistic processing, via simulation and analysis. The achieved results show that the realistic feedback-aided protocols with deterministic power selection can support 12.8 grant-free users per slot guaranteeing a packet loss rate of 10−4while a massive MIMO base station equipped with 128 antennas is employed

In the implementation of quantum information systems, one type of Pauli error, such as phase-flip errors, may occur more frequently than others, like bit-flip errors. For this reason, quantum error-correcting codes that handle asymmetric errors are critical to mitigating the impact of such impairments. To this aim, several asymmetric quantum codes have been proposed. These include variants of surface codes like the XZZX and ZZZY surface codes, tailored to preserve quantum information in the presence of error asymmetries. In this work, we propose two classes of Calderbank, Shor and Steane (CSS) topological codes, referred to as cylindrical and Möbius codes, particular cases of the fiber bundle family. Cylindrical codes maintain a fully planar structure, while Möbius codes are quasi-planar, with minimal non-local qubit interactions. We construct these codes employing the algebraic chain complexes formalism, providing theoretical upper bounds for the logical error rate. Our results demonstrate that cylindrical and Möbius codes outperform standard surface codes when using the minimum weight perfect matching (MWPM) decoder.

This paper elaborates on the idea of building grant-free channel access schemes from non-orthogonal multiple access ones, and proposes an explicit such scheme based on sparse code multiple access (SCMA). In the designed protocol, SCMA codebooks and pilots are chosen by users in a fully uncoordinated fashion, with multiple pilots associated with the same codebook to aid codebook detection. A modified two-stage SCMA decoder is proposed, where a low-complexity collision resolution algorithm, working on a super-constellation, and an SCMA message passing detector are iteratively applied. Numerical results, integrated by analysis in the high signal-to-noise ratio regime, highlight a potential for the proposed scheme in the context of massive uncoordinated machine-type uplink.

Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used PauliXor PauliZoperators in a square structure, these codes can be improved by rotating the lattice or incorporating a mix of generators in the XZZX variant. However, a comprehensive theoretical analysis of the logical error rate for these variants has been lacking. To address this gap, we present theoretical formulas based on recent advancements in understanding the weight distribution of stabilizer codes. For example, over an asymmetric channel with asymmetryA= 10 and a physical error ratep→ 0, we observe that the logical error rate asymptotically approachespL→ 10p2for the rotated [[9, 1, 3]] XZZX code andpL→ 18.3p2for the [[13, 1, 3]] surface code. Additionally, we observe a particular behavior regarding rectangular lattices in the presence of asymmetric channels. Our findings demonstrate that implementing both rotation and XZZX modifications simultaneously can lead to suboptimal performance. Thus, in scenarios involving a rectangular lattice, it is advisable to avoid using both modifications simultaneously.

One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing and quantum Internet. We here analyze the performance of surface codes, one of the most important class for practical implementations, on both symmetric and asymmetric quantum channels. We derive approximate expressions, confirmed by simulations, to evaluate the performance of surface codes and of XZZX codes, and provide a metric to assess the advantage of codes with respect to uncoded systems. Our findings allow to characterize the performance by means of analytical formulas of surface codes, like, for example, the [[13, 1, 3]], the [[23, 1, 3/5]], the [[33, 1, 3/7]], and the [[41, 1, 5]] surface codes.

In this paper, new coded random access schemes for massive IoT, capable of accommodating a non-instantaneous feedback from the receiver, are developed. The proposed schemes are based on the introduction of waiting slots between any two consecutive replicas transmitted by the same active device. The waiting window can be exploited by the device to receive acknowledgment messages that, otherwise, would consume uplink resources with a consequent performance degradation. The achievable performance of the developed schemes is investigated, by analysis and simulation, over a realistic wireless channel model and realistic signal processing at the base station, showing negligible losses with respect to previously proposed coded random access systems with idealized instantaneous feedback.

In next generation Internet-of-Things, the overhead introduced by grant-based multiple access protocols may engulf the access network as a consequence of the unprecedented number of connected devices. Grant-free access protocols are therefore gaining an increasing interest to support massive access from machine-type devices with intermittent activity. In this paper, coded random access (CRA) with massive multiple input multiple output (MIMO) is investigated as a solution to design highly-scalable massive multiple access protocols, taking into account stringent requirements on latency and reliability. With a focus on signal processing aspects at the physical layer and their impact on the overall system performance, critical issues of successive interference cancellation (SIC) over fading channels are first analyzed. Then, SIC algorithms and a scheduler are proposed that can overcome some of the limitations of the current access protocols. The effectiveness of the proposed processing algorithms is validated by Monte Carlo simulation, for different CRA protocols and by comparisons with developed benchmarks.

Grant-free access schemes are candidates to support future massive multiple access applications owing to their capability to reduce control signaling and latency. As a promising class of grant-free schemes, coded random access schemes can achieve high reliabilities also with uncoordinated transmissions and therefore in presence packet collisions. In this paper, an analysis tool for coded random access, based on density evolution, is proposed and exploited for system design and optimization. In sharp contrast with the existing literature, where such tools have been developed under simplified channel assumptions, the proposed tool captures not only MAC layer features, but also the physical wireless fading channel and a realistic physical layer signal processing based on multiple antennas and randomlychosen orthogonal pilots. Theoretical results are validated by comparison with symbol-level Monte Carlo simulations.

The design of highly scalable multiple access schemes is a main challenge in the evolution towards future massive machine-type communications, where reliability and latency constraints must be ensured to a large number of uncoordinated devices. In this scenario, coded random access (CRA) schemes, where successive interference cancellation algorithms allow large improvements with respect to classical random access protocols, have recently attracted an increasing interest. Impressive performance can be potentially obtained by combining CRA with massive multiple input multiple output (MIMO). In this paper we provide an analysis of such schemes focusing on the effects of imperfect channel estimation on successive interference cancellation. Based on the analysis we then propose an innovative signal processing algorithm for CRA in massive MIMO systems.

An information-theoretic approach to irregular repetition slotted ALOHA (IRSA) is proposed. In contrast with previous works, in which IRSA analysis is conducted only based on quantities that are typical of collision models such as the traffic, the new approach also captures more fundamental quantities. Specifically, a suitable codebook construction for the adder channel model is adopted to establish a link with successive interference cancellation over the multi-packet reception channel. This perspective allows proving achievability and converse results for the average sum rate of IRSA multiple access schemes.

Massive multiple access schemes, capable of serving a large number of uncoordinated devices while fulfilling reliability and latency constraints, are proposed. The schemes belong to the class of grant-free coded random access protocols and are tailored to massive multiple input multiple output (MIMO) base station processing. High reliability is obtained owing to an intra-frame spatial coupling effect, triggered by a simple device access protocol combined with acknowledgements (ACKs) from the base station. To provide system design guidelines, analytical bounds on error floor and latency are also derived. The proposed schemes are particularly interesting to address the challenges of massive machine-type communications in the framework of next generation massive multiple access systems.

Networks of randomly distributed nodes appear in various fields, including forestry and wireless communications, and can often be modeled, using stochastic geometry theory, as Poisson point processs (PPPs). In these contexts, estimation of nodes density is important for monitoring and optimizing the network. Originally, this problem has been addressed in forestry where the trees are the nodes and, assuming these are distributed according to an infinite two-dimensional homogeneous PPP, the spatial density can be estimated by measuring the distances from one reference tree to its neighbors. However, in many other scenarios, nodes could result invisible with some probability, for example depending on distance. In this paper, we derive the Cramér-Rao bounds and new estimators for the node spatial density, taking into account a limited capability in sensing neighbors. As an example, we provide estimators of the spatial density of transmitting devices in wireless networks with links affected by thermal noise, path loss, and shadowing.

Owing to the extremely narrow beams, a main issue in optical deep space communications is represented by miss-pointing errors, which may severely degrade the system performance and availability. In this paper, we address pointing losses in the case in which both the receiver and the transmitter are affected by angular errors. Pointing losses are evaluated through two approaches. The first approach is deterministic and only requires knowledge of a maximum angular error. The second approach requires knowledge of the angular error statistical distribution and tackles the problem from an outage probability viewpoint. These tools are then applied to analyze the impact of pointing losses in deep space optical links in which both terminals suffer from miss-pointing effects. The antenna gains are first optimized to maximize the effective system gain. The optimum antenna gains are then applied to evaluate maximum achievable ranges and to perform link design by means of optical link budgets.