arXiv subjects

Olav Tirkkonen

Publications and source records attributed to Olav Tirkkonen.

At least 19 recordsLinked to original sources

arXiv2026

Input-Correlated Supervision Noise Limits the Benefits of OTA Training for Learned Receivers

While learned wireless receivers are typically studied using synthetic data, the impact of over-the-air (OTA) measurements for training remains unclear. We conducted a 5.88 GHz measurement campaign with a 5G/6G-like orthogonal frequency-division multiplexing (OFDM) system across diverse environments and mobility conditions, and trained a neural channel estimator and a capacity-matched end-to-end neural receiver using mixtures of measured and synthetic data. Increasing the OTA fraction revealed a fundamental asymmetry: measured data consistently improved the end-to-end receiver, whereas the channel estimator peaked at an intermediate fraction and degraded with fully measured training. We showed that this difference arises from the supervision target: OTA channel labels are derived from noisy received signals and therefore contain supervision errors correlated with the receiver input, whereas decoded bits validated by a cyclic redundancy check (CRC) provide effectively error-free supervision. A controlled denoising experiment confirmed that this correlation, rather than limited data diversity, caused the degradation. These results provide practical guidance for training learned receivers with OTA data: end-to-end receivers benefit from fully measured training, whereas channel estimators benefit from moderate OTA fractions but require improved label quality, e.g. via denoising, to unlock further gains.

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arXiv2025

Transversal Toffoli-gate in Hybrid-code System

We study the transversality of the Toffoli gate in a hybrid-code system that employs two quantum error correction codes with special structure. We find that a system using a triorthogonal code with its paired code supports a fully transversal implementation of the Toffoli gate. Through circuit-level analysis, we prove the transversality of the Toffoli operation in this system. Based on this hybrid-code framework, we propose a Toffoli state distillation protocol that does not rely on pre-distilled $\mathbf{T}$-gate magic states. In our approach, the Toffoli state is directly distilled layer by layer within the hybrid-code system using only transversal operations. Numerical simulations demonstrate that our method uses approximately 50\% fewer qubit resources than previously reported protocols.

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arXiv2025

Bounds in the Projective Unitary Group with Respect to Global Phase Invariant Metric

We consider a global phase-invariant metric in the projective unitary group PUn, relevant for universal quantum computing. We obtain the volume and measure of small metric ball in PUn and derive the Gilbert-Varshamov and Hamming bounds in PUn. In addition, we provide upper and lower bounds for the kissing radius of the codebooks in PUn as a function of the minimum distance. Using the lower bound of the kissing radius, we find a tight Hamming bound. Also, we establish bounds on the distortion-rate function for quantizing a source uniformly distributed over PUn. As example codebooks in PUn, we consider the projective Pauli and Clifford groups, as well as the projective group of diagonal gates in the Clifford hierarchy, and find their minimum distances. For any code in PUn with given cardinality we provide a lower bound of covering radius. Also, we provide expected value of the covering radius of randomly distributed points on PUn, when cardinality of code is sufficiently large. We discuss codebooks at various stages of the projective Clifford + T and projective Clifford + S constructions in PU2, and obtain their minimum distance, distortion, and covering radius. Finally, we verify the analytical results by simulation.

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arXiv2025

Low Overhead Universal Quantum Computation with Triorthogonal Codes

We study the use of triorthogonal codes for universal fault-tolerant quantum computation and propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both universality and a transversal gate set. We show that our methods reduce the resource overhead compared with existing fault-tolerant protocols. We develop a simple fault-tolerant implementation of the logical Hadamard gate for triorthogonal codes by exploiting the fact that they have transversal controlled-Z (CZ) gates, resulting in a circuit with reduced overhead. We also introduce a procedure for generating a symmetric Calderbank-Shor-Steane code paired with a triorthogonal code, which allows CNOT and CZ gate transversality across the pair of codes. In addition, we present logical state teleportation circuits that transfer encoded states between the two codes, allowing all logical operations to be performed transversally. Our methods can be integrated into the Steane error correction framework without incurring additional resource cost. Finally, using the 15-qubit code as an example, we demonstrate that our protocols significantly reduce the gate overhead compared with other existing methods. These results highlight the potential of combining distinct code structures to achieve low-overhead, universal fault-tolerant quantum computation.

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arXiv2024

On Transversality Across Two Distinct Quantum Error Correction Codes For Quantum Repeaters

In this paper, we investigate the transversality of pairs of CSS codes and their use in the second generation of quantum repeaters (QR)s. We show that different stations of quantum link can experience different errors. Considering this fact, we suggest to use different CSS codes in different stations. We also suggest to use $[[n, k]]$ codes with $k > 1$ as they are more efficient then codes with $k = 1$. We establish sufficient and necessary conditions for a pair of CSS codes to be non-local CNOT-transversal. We show that in contrast to the well known CNOT transversality which states that two CSS codes should be the same, less restrictive constraints are needed. Next, we establish sufficient and necessary conditions for a code pair to be CZ-transversal.

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arXiv2024

Deterministic Patterns for Multiple Access with Latency and Reliability Guarantees

We study a scenario in which multiple uncoordinated devices aim to achieve reliable transmissions within a given time frame. The devices are intermittently active and access a shared pool of channel resources in a grant-free manner by utilizing multiple transmissions (K-repetition coding). This allows them to achieve diversity and improve the reliability within a certain latency constraint. We focus on two access methods: one where devices choose K slots at random and another one where the access patterns are deterministic and follow a specific code design, namely the Steiner System. We analyze the problem under two signal models that involve different complexity for the receiver. First, collision model is considered, where only interference-free transmissions can be used and combined. Second, a model treating interference as noise is analyzed, where the receiver is capable of utilizing all K replicas, applying maximum ratio combining (MRC). For both signal models, we investigate receivers with and without successive interference cancellation (SIC). We develop approximations and bounds for the outage probabilities that very closely match simulation results. Overall, we show that deterministic access patterns have the potential to significantly outperform random selection in terms of reliability. Furthermore, deterministic access patterns offer a simplified system design.

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arXiv2023

Channel Charting for Streaming CSI Data

Channel charting (CC) applies dimensionality reduction to channel state information (CSI) data at the infrastructure basestation side with the goal of extracting pseudo-position information for each user. The self-supervised nature of CC enables predictive tasks that depend on user position without requiring any ground-truth position information. In this work, we focus on the practically relevant streaming CSI data scenario, in which CSI is constantly estimated. To deal with storage limitations, we develop a novel streaming CC architecture that maintains a small core CSI dataset from which the channel charts are learned. Curation of the core CSI dataset is achieved using a min-max-similarity criterion. Numerical validation with measured CSI data demonstrates that our method approaches the accuracy obtained from the complete CSI dataset while using only a fraction of CSI storage and avoiding catastrophic forgetting of old CSI data.

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arXiv2023

Model-based Deep Learning for Beam Prediction based on a Channel Chart

Channel charting builds a map of the radio environment in an unsupervised way. The obtained chart locations can be seen as low-dimensional compressed versions of channel state information that can be used for a wide variety of applications, including beam prediction. In non-standalone or cell-free systems, chart locations computed at a given base station can be transmitted to several other base stations (possibly operating at different frequency bands) for them to predict which beams to use. This potentially yields a dramatic reduction of the overhead due to channel estimation or beam management, since only the base station performing charting requires channel state information, the others directly predicting the beam from the chart location. In this paper, advanced model-based neural network architectures are proposed for both channel charting and beam prediction. The proposed methods are assessed on realistic synthetic channels, yielding promising results.

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arXiv2023

Wireless Channel Charting: Theory, Practice, and Applications

Channel charting is a recently proposed framework that applies dimensionality reduction to channel state information (CSI) in wireless systems with the goal of associating a pseudo-position to each mobile user in a low-dimensional space: the channel chart. Channel charting summarizes the entire CSI dataset in a self-supervised manner, which opens up a range of applications that are tied to user location. In this article, we introduce the theoretical underpinnings of channel charting and present an overview of recent algorithmic developments and experimental results obtained in the field. We furthermore discuss concrete application examples of channel charting to network- and user-related applications, and we provide a perspective on future developments and challenges as well as the role of channel charting in next-generation wireless networks.

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arXiv2023

Modular CSI Quantization for FDD Massive MIMO Communication

We consider high-dimensional MIMO transmissions in frequency division duplexing (FDD) systems. For precoding, the frequency selective channel has to be measured, quantized and fed back to the base station by the users. When the number of antennas is very high this typically leads to prohibitively high quantization complexity and large feedback. In 5G New Radio (NR), a modular quantization approach has been applied for this, where first a low-dimensional subspace is identified for the whole frequency selective channel, and then subband channels are linearly mapped to this subspace and quantized. We analyze how the components in such a modular scheme contribute to the overall quantization distortion. Based on this analysis we improve the technology components in the modular approach and propose an orthonormalized wideband precoding scheme and a sequential wideband precoding approach which provide considerable gains over the conventional method. We compare the performance of the developed quantization schemes to prior art by simulations in terms of the projection distortion, overall distortion and spectral efficiency, in a scenario with a realistic spatial channel model.

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arXiv2022

Channel Charting Aided Pilot Reuse for Massive MIMO Systems with Spatially Correlated Channels

Massive multiple-input multiple-output (mMIMO) technology is a way to increase the spectral efficiency of machine-type communications (MTC). To exploit the benefits from large antenna arrays, accurate channel estimation through pilot signals is needed. Massive MTC systems cannot avoid pilot reuse due to the enormous numbers of connected devices. We propose a pilot reuse algorithm based on channel charting (CC) to mitigate pilot contamination in a multi-sector single-cell massive MTC system having spatially correlated channels. We show that after creating an interference map via CC, a simple strategy to allocate the pilot sequences can be implemented. The simulation results show that the CC-based pilot reuse strategy improves channel estimation accuracy, which subsequently improves the symbol detection performance and increases the spectral efficiency compared to other existing schemes. Moreover, the performance of the CC pilot assignment method approaches that of exhaustive search pilot assignment for small network setups.

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arXiv2022

Optimal Bandwidth Allocation for Multicast-Cache-Aided on-Demand Streaming in Wireless Networks

We consider a hybrid delivery scheme for streaming content, combining cache-enabled Orthogonal Multipoint Multicast (OMPMC) and on-demand Single-Point Unicast (SPUC) transmissions for heterogeneous networks. The OMPMC service transmits cached files through the whole network to interested users, and users not being satisfied by this service are assigned to the SPUC service to be individually served. The SPUC fetches the requested files from the core network and unicasts them to UEs using cellular beamforming transmissions. We optimize the delivery scheme to minimize the average resource consumption in the network. We formulate a constrained optimization problem over the cache placement and resource allocation of the OMPMC component, as well as the multi-user beamforming scheme of the SPUC component. We apply a path-following method to find the optimal traffic offloading solution. The solutions portray a contrast between the total amount of consumed resources and service outage probability. Simulation results show that the hybrid scheme provides a better tradeoff between the amount of network-wide consumed resources and the service outage probability, as compared to schemes from the literature.

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arXiv2021

Joint Channel Estimation and Data Detection in Cell-Free Massive MU-MIMO Systems

We propose a joint channel estimation and data detection (JED) algorithm for densely-populated cell-free massive multiuser (MU) multiple-input multiple-output (MIMO) systems, which reduces the channel training overhead caused by the presence of hundreds of simultaneously transmitting user equipments (UEs). Our algorithm iteratively solves a relaxed version of a maximum a-posteriori JED problem and simultaneously exploits the sparsity of cell-free massive MU-MIMO channels as well as the boundedness of QAM constellations. In order to improve the performance and convergence of the algorithm, we propose methods that permute the access point and UE indices to form so-called virtual cells, which leads to better initial solutions. We assess the performance of our algorithm in terms of root-mean-squared-symbol error, bit error rate, and mutual information, and we demonstrate that JED significantly reduces the pilot overhead compared to orthogonal training, which enables reliable communication with short packets to a large number of UEs.

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arXiv2021

Fundamental Rate-Memory Tradeoff for Coded Caching in Presence of User Inactivity

Coded caching utilizes proper file subpacketization and coded delivery to make full use of the multicast opportunities in content delivery, to alleviate file transfer load in massive content delivery scenarios. Most existing work considers deterministic environments. An important practical topic is to characterize the impact of the uncertainty from user inactivity on coded caching. We consider a one server cache-enabled network under homogeneous file and network settings in presence of user inactivity. Unlike random or probabilistic caching studied in the literature, deterministic coded caching is considered, with the objective to minimize the worst-case backhaul load by optimizing the file subpacketization and the caching strategy. First, a coded caching method is used, where each file is split into the same type of fragments labeled using sets with fixed cardinality, and the optimality of the selected cardinality is proved. Optimal file subpacketization by splitting the file into multiple types of fragments labeled with multiple cardinalities is then discussed. We show that the closed-form optimum turns out to be given by a fixed cardinality -- optimizing for user inactivity only affects file delivery, cache placement is not affected. A decentralized version is also discussed and analyzed, where each user fills its storage independently at random without centralized coordination, and user inactivity is taken into account in file delivery. Simulation results show that the optimization based centralized coded caching scheme provides performance comparable to the ideal scenario assuming full knowledge of user inactivity in the placement phase, while decentralized caching performs slightly worse against user inactivity.

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arXiv2021

Exploiting Spatial Correlation for Pilot Reuse in Single-Cell mMTC

As a key enabler for massive machine-type communications (mMTC), spatial multiplexing relies on massive multiple-input multiple-output (mMIMO) technology to serve the massive number of user equipments (UEs). To exploit spatial multiplexing, accurate channel estimation through pilot signals is needed. In mMTC systems, it is impractical to allocate a unique orthogonal pilot sequence to each UE as it would require too long pilot sequences, degrading the spectral efficiency. This work addresses the design of channel features from correlated fading channels to assist the pilot assignment in multi-sector mMTC systems under pilot reuse of orthogonal sequences. In order to reduce pilot collisions and to enable pilot reuse, we propose to extract features from the channel covariance matrices that reflect the level of orthogonality between the UEs channels. Two features are investigated: covariance matrix distance (CMD) feature and CMD-aided channel charting (CC) feature. In terms of symbol error rate and achievable rate, the CC-based feature shows superior performance than the CMD-based feature and baseline pilot assignment algorithms.

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arXiv2021

Binary Subspace Chirps

We describe in details the interplay between binary symplectic geometry and quantum computation, with the ultimate goal of constructing highly structured codebooks. The Binary Chirps (BCs) are Complex Grassmannian Lines in $N = 2^m$ dimensions used in deterministic compressed sensing and random/unsourced multiple access in wireless networks. Their entries are fourth roots of unity and can be described in terms of second order Reed-Muller codes. The Binary Subspace Chirps (BSSCs) are a unique collection of BCs of $\textit{ranks}$ ranging from $r=0$ to $r = m$, embedded in $N$ dimensions according to an on-off pattern determined by a rank $r$ binary subspace. This yields a codebook that is asymptotically 2.38 times larger than the codebook of BCs, has the same minimum chordal distance as the codebook of BCs, and the alphabet is minimally extended from $\{\pm 1,\pm i\}$ to $\{\pm 1,\pm i, 0\}$. Equivalently, we show that BSSCs are stabilizer states, and we characterize them as columns of a well-controlled collection of Clifford matrices. By construction, the BSSCs inherit all the properties of BCs, which in turn makes them good candidates for a variety of applications. For applications in wireless communication, we use the rich algebraic structure of BSSCs to construct a low complexity decoding algorithm that is reliable against Gaussian noise. In simulations, BSSCs exhibit an error probability comparable or slightly lower than BCs, both for single-user and multi-user transmissions.

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arXiv2021

Decomposition of Clifford Gates

In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate. To achieve this goal, we exploit the structure of the symplectic group with a novel graphical approach.

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arXiv2020

Un-Weyl-ing the Clifford Hierarchy

The teleportation model of quantum computation introduced by Gottesman and Chuang (1999) motivated the development of the Clifford hierarchy. Despite its intrinsic value for quantum computing, the widespread use of magic state distillation, which is closely related to this model, emphasizes the importance of comprehending the hierarchy. There is currently a limited understanding of the structure of this hierarchy, apart from the case of diagonal unitaries (Cui et al., 2017; Rengaswamy et al. 2019). We explore the structure of the second and third levels of the hierarchy, the first level being the ubiquitous Pauli group, via the Weyl (i.e., Pauli) expansion of unitaries at these levels. In particular, we characterize the support of the standard Clifford operations on the Pauli group. Since conjugation of a Pauli by a third level unitary produces traceless Hermitian Cliffords, we characterize their Pauli support as well. Semi-Clifford unitaries are known to have ancilla savings in the teleportation model, and we explore their Pauli support via symplectic transvections. Finally, we show that, up to multiplication by a Clifford, every third level unitary commutes with at least one Pauli matrix. This can be used inductively to show that, up to a multiplication by a Clifford, every third level unitary is supported on a maximal commutative subgroup of the Pauli group. Additionally, it can be easily seen that the latter implies the generalized semi-Clifford conjecture, proven by Beigi and Shor (2010). We discuss potential applications in quantum error correction and the design of flag gadgets.

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