arXiv subjects

Bane Vasic

Publications and source records attributed to Bane Vasic.

At least 19 recordsLinked to original sources

arXiv2026

Trapping Sets of Detector Error Models

Message-passing decoders are among the most promising candidates for scalable quantum error correction, yet their behavior in the low-error-rate regime remains poorly understood under realistic circuit-level noise. In this work, we introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor. We apply exhaustive trapping-set enumeration directly to the detector error model of a bivariate bicycle code and test all low-weight fault configurations supported on the resulting structures. This converts the analysis of extremely rare logical failures into a finite structural search, avoiding the prohibitive cost of direct Monte Carlo simulation. We evaluate the framework on three iterative decoders with substantially different architectures and decoding heuristics. Remarkably, for \texttt{RelayBP}, the resulting prediction accurately reproduces the simulated error floor; for the others, it remains within the same order of magnitude. Despite their differences, leafless elementary trapping sets capture a substantial part of the low-weight error-floor contribution for all three decoders. Moreover, each decoder admits failures caused by fault configurations well below the correction capability implied by the circuit-level distance, revealing a substantial gap between code distance and practical iterative-decoding performance. These results establish trapping-set analysis as a practical framework for predicting error floors, exposing the structural weaknesses of iterative decoders, and guiding the joint design of decoding algorithms.

quant-ph↗

arXiv2025

Quantum Low-Density Parity-Check Codes

Quantum error correction (QEC) is a cornerstone of quantum computing, enabling reliable information processing in the presence of noise. Sparse stabilizer codes -- referred to generally as quantum low-density parity-check (QLDPC) codes -- have risen to the forefront of QEC research in recent years. This can be attributed to several key factors. First, classical LDPC codes admit low-complexity belief propagation iterative decoding and near-capacity performance, which contributed to the early interest in QLDPC codes. Then, the result promising constant overhead fault tolerance using QLDPC codes led to the search for code families that go beyond the long-holding $\sqrt{n}$ scaling barrier of minimum distance for codelength $n$. This resulted in recent breakthroughs in the construction of QLDPC codes, which, combined with efficient decoding algorithms and the development of fault-tolerant protocols operating on QLDPC-encoded quantum information, provide a promising pathway to low-overhead, fault-tolerant quantum computation. However, despite their potential, challenges remain, particularly in constructing and decoding finite-length codes that account for, or efficiently leverage, specific characteristics of quantum hardware, such as connectivity, topology, native gate sets, and noise models. This article provides an in-depth examination of QLDPC codes and their iterative decoders, catering to an information theory audience with no or limited background in quantum mechanics. We discuss the theoretical underpinnings, explore unique characteristics of quantum channels, and delineate key code constructions and decoding algorithms, ultimately highlighting the impact and future prospects of QLDPC codes in quantum information science.

quant-ph↗

arXiv2025

Action-List Reinforcement Learning Syndrome Decoding for Binary Linear Block Codes

This paper explores the application of reinforcement learning techniques to enhance the performance of decoding of linear block codes based on flipping bits and finding optimal decisions. We describe the methodology for mapping the iterative decoding process into Markov Decision Processes (MDPs) and propose different methods to reduce the number of states in the MDP. A truncated MDP is proposed to reduce the number of states in the MDP by learning a Hamming ball with a specified radius around codewords. We then propose a general scheme for reinforcement learning based decoders applicable to any class of codes to improve the performance of decoders. We call this scheme an action-list decoding. We design an action-list decoder based on the Deep-Q network values that substantially enhance performance. We also get benefit of automorphism group of code to further improve the code performance. Additionally, we propose a feedback-based method to exploit and enhance the performance of existing high-performing decoders by applying reinforcement learning algorithms after the existing decoders. These approaches effectively reduces the complexity of the reinforcement learning block. Finally, we present experimental results for the Low-Density Parity Check (LDPC) codes over the Binary Symmetric Channel (BSC) to demonstrate the efficiency of the proposed methods.

cs.IT↗

arXiv2025

Fault Tolerant Decoding of QLDPC-GKP Codes with Circuit Level Soft Information

Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome measurements of an inner bosonic code is used to inform decoding for an outer code layer consisting of a discrete-variable stabilizer code such as a surface code. The use of Quantum Low-Density Parity Check (QLDPC) codes as an outer code is of particular interest due to the significantly higher encoding rates offered by these code families, leading to a further reduction in overhead for large-scale quantum computing. Recent works have investigated the performance of QLDPC-GKP codes in detail, and the use of analog information from the inner code significantly boosts decoder performance. However, the noise models assumed in these works are typically limited to depolarizing or phenomenological noise. In this paper, we investigate the performance of QLDPC-GKP concatenated codes under circuit-level noise, based on a model introduced by Noh et al. in the context of the surface-GKP code. To demonstrate the performance boost from analog information, we investigate three scenarios: (a) decoding without soft information, (b) decoding with precomputed error probabilities but without real-time soft information, and (c) decoding with real-time soft information obtained from round-to-round decoding of the inner GKP code. Results show minimal improvement between (a) and (b), but a significant boost in (c), indicating that real-time soft information is critical for concatenated decoding under circuit-level noise. We also study the effect of measurement schedules with varying depths and show that using a schedule with minimum depth is essential for obtaining reliable soft information from the inner code.

quant-ph↗

arXiv2025

Turbo-Annihilation of Hook Errors in Stabilizer Measurement Circuits

We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner graph that includes every possible source of noise. However, this results in a highly irregular graph with many short cycles, leading to poor performance of message-passing algorithms. To compensate, ordered statistics decoding is typically employed, but its cubic complexity renders it impractical for large codes or repeated stabilizer measurements. Our approach instead focuses on estimating the effective data errors caused by hook faults, modeling them as memory channels. We integrate trellis-based soft-input soft-output equalizers into the Tanner graph of the code, and show that the resulting decoding graph preserves the structural properties of the original Tanner graph such as node degree and girth, enabling efficient message passing. Applied to bivariate bicycle quantum LDPC codes, our decoder outperforms standard belief propagation on the circuit-level graph and closely approaches OSD0 performance, all while maintaining linear complexity and scalability.

quant-ph↗

arXiv2025

Construction and Decoding of Quantum Margulis Codes

Quantum low-density parity-check codes are a promising approach to fault-tolerant quantum computation, offering potential advantages in rate and decoding efficiency. In this work, we introduce quantum Margulis codes, a new class of QLDPC codes derived from Margulis' classical LDPC construction via the two-block group algebra framework. We show that quantum Margulis codes, unlike bivariate bicycle codes which require ordered statistics decoding for effective error correction, can be efficiently decoded using a standard min-sum decoder with linear complexity, when decoded under the code capacity noise model. This is attributed to their Tanner graph structure, which does not exhibit group symmetry, thereby mitigating the well-known problem of error degeneracy in QLDPC decoding. To further enhance performance, we propose an algorithm for constructing 2BGA codes with controlled girth, ensuring a minimum girth of 6 or 8, and use it to generate several quantum Margulis codes of length 240 and 642. We validate our approach through numerical simulations, demonstrating that quantum Margulis codes behave significantly better than BB codes in the error floor region, under min-sum decoding.

quant-ph↗

arXiv2025

Enhanced Min-Sum Decoding of Quantum Codes Using Previous Iteration Dynamics

In this paper, we propose a novel message-passing decoding approach that leverages the degeneracy of quantum low-density parity-check codes to enhance decoding performance, eliminating the need for serial scheduling or post-processing. Our focus is on two-block Calderbank-Shor-Steane (CSS) codes, which are composed of symmetric stabilizers that hinder the performance of conventional iterative decoders with uniform update rules. Specifically, our analysis shows that, under the isolation assumption, the min-sum decoder fails to converge when constant-weight errors are applied to symmetric stabilizers, as variable-to-check messages oscillate in every iteration. To address this, we introduce a decoding technique that exploits this oscillatory property by applying distinct update rules: variable nodes in one block utilize messages from previous iterations, while those in the other block are updated conventionally. Logical error-rate results demonstrate that the proposed decoder significantly outperforms the normalized min-sum decoder and achieves competitive performance with belief propagation enhanced by order-zero ordered statistics decoding, all while maintaining linear complexity in the code's block length.

quant-ph↗

arXiv2024

Quantum Margulis Codes

Recently, Lin and Pryadko presented the quantum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations.

quant-ph↗

arXiv2024

Generalization Bounds for Neural Belief Propagation Decoders

Machine learning based approaches are being increasingly used for designing decoders for next generation communication systems. One widely used framework is neural belief propagation (NBP), which unfolds the belief propagation (BP) iterations into a deep neural network and the parameters are trained in a data-driven manner. NBP decoders have been shown to improve upon classical decoding algorithms. In this paper, we investigate the generalization capabilities of NBP decoders. Specifically, the generalization gap of a decoder is the difference between empirical and expected bit-error-rate(s). We present new theoretical results which bound this gap and show the dependence on the decoder complexity, in terms of code parameters (blocklength, message length, variable/check node degrees), decoding iterations, and the training dataset size. Results are presented for both regular and irregular parity-check matrices. To the best of our knowledge, this is the first set of theoretical results on generalization performance of neural network based decoders. We present experimental results to show the dependence of generalization gap on the training dataset size, and decoding iterations for different codes.

cs.IT↗

arXiv2024

Progressive-Proximity Bit-Flipping for Decoding Surface Codes

Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently remains a challenge: existing decoders often fall short of meeting requirements such as having low computational complexity (ideally linear in the code's blocklength), low decoding latency, and low power consumption. In this paper we propose a novel bit-flipping (BF) decoder tailored for toric and surface codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting degenerate multiple errors on adjacent qubits. Our algorithm has quadratic complexity growth and it can be efficiently implemented as it does not require operations on dynamic memories, as do state-of-art decoding algorithms such as minimum weight perfect matching or union find. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code and 7% for the rotated planar code over the binary symmetric channel.

quant-ph↗

arXiv2024

Low-Complexity Linear Programming Based Decoding of Quantum LDPC codes

This paper proposes two approaches for reducing the impact of the error floor phenomenon when decoding quantum low-density parity-check codes with belief propagation based algorithms. First, a low-complexity syndrome-based linear programming (SB-LP) decoding algorithm is proposed, and second, the proposed SB-LP is applied as a post-processing step after syndrome-based min-sum (SB-MS) decoding. For the latter case, a new early stopping criterion is introduced to decide when to activate the SB-LP algorithm, avoiding executing a predefined maximum number of iterations for the SB-MS decoder. Simulation results show, for a sample hypergraph code, that the proposed decoder can lower the error floor by two to three orders of magnitude compared to SB-MS for the same total number of decoding iterations.

cs.IT↗

arXiv2023

Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to implement such codes makes their physical realization challenging. Here, we propose a hardware-efficient scheme to perform fault-tolerant quantum computation with high-rate qLDPC codes on reconfigurable atom arrays, directly compatible with recently demonstrated experimental capabilities. Our approach utilizes the product structure inherent in many qLDPC codes to implement the non-local syndrome extraction circuit via atom rearrangement, resulting in effectively constant overhead in practically relevant regimes. We prove the fault tolerance of these protocols, perform circuit-level simulations of memory and logical operations with these codes, and find that our qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits at a realistic physical error rate of $10^{-3}$. We further find that less than 3000 physical qubits are sufficient to obtain over an order of magnitude qubit savings compared to the surface code, and quantum algorithms involving thousands of logical qubits can be performed using less than $10^5$ physical qubits. Our work paves the way for explorations of low-overhead quantum computing with qLDPC codes at a practical scale, based on current experimental technologies.

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arXiv2023

Neuro-OSVETA: A Robust Watermarking of 3D Meshes

Best and practical watermarking schemes for copyright protection of 3D meshes are required to be blind and robust to attacks and errors. In this paper, we present the latest developments in 3D blind watermarking with a special emphasis on our Ordered Statistics Vertex Extraction and Tracing Algorithm (OSVETA) algorithm and its improvements. OSVETA is based on a combination of quantization index modulation (QIM) and error correction coding using novel ways for judicial selection of mesh vertices which are stable under mesh simplification, and the technique we propose in this paper offers a systematic method for vertex selection based on neural networks replacing a heuristic approach in the OSVETA. The Neuro-OSVETA enables a more precise mesh geometry estimation and better curvature and topological feature estimation. These enhancements result in a more accurate identification of stable vertices resulting in significant reduction of deletion probability.

cs.MM↗

arXiv2021

FAID Diversity via Neural Networks

Decoder diversity is a powerful error correction framework in which a collection of decoders collaboratively correct a set of error patterns otherwise uncorrectable by any individual decoder. In this paper, we propose a new approach to design the decoder diversity of finite alphabet iterative decoders (FAIDs) for Low-Density Parity Check (LDPC) codes over the binary symmetric channel (BSC), for the purpose of lowering the error floor while guaranteeing the waterfall performance. The proposed decoder diversity is achieved by training a recurrent quantized neural network (RQNN) to learn/design FAIDs. We demonstrated for the first time that a machine-learned decoder can surpass in performance a man-made decoder of the same complexity. As RQNNs can model a broad class of FAIDs, they are capable of learning an arbitrary FAID. To provide sufficient knowledge of the error floor to the RQNN, the training sets are constructed by sampling from the set of most problematic error patterns - trapping sets. In contrast to the existing methods that use the cross-entropy function as the loss function, we introduce a frame-error-rate (FER) based loss function to train the RQNN with the objective of correcting specific error patterns rather than reducing the bit error rate (BER). The examples and simulation results show that the RQNN-aided decoder diversity increases the error correction capability of LDPC codes and lowers the error floor.

cs.IT↗

arXiv2016

Check-hybrid GLDPC Codes: Systematic Elimination of Trapping Sets and Guaranteed Error Correction Capability

In this paper, we propose a new approach to construct a class of check-hybrid generalized low-density parity-check (CH-GLDPC) codes which are free of small trapping sets. The approach is based on converting some selected check nodes involving a trapping set into super checks corresponding to a 2-error correcting component code. Specifically, we follow two main purposes to construct the check-hybrid codes; first, based on the knowledge of the trapping sets of the global LDPC code, single parity checks are replaced by super checks to disable the trapping sets. We show that by converting specified single check nodes, denoted as critical checks, to super checks in a trapping set, the parallel bit flipping (PBF) decoder corrects the errors on a trapping set and hence eliminates the trapping set. The second purpose is to minimize the rate loss caused by replacing the super checks through finding the minimum number of such critical checks. We also present an algorithm to find critical checks in a trapping set of column-weight 3 LDPC code and then provide upper bounds on the minimum number of such critical checks such that the decoder corrects all error patterns on elementary trapping sets. Moreover, we provide a fixed set for a class of constructed check-hybrid codes. The guaranteed error correction capability of the CH-GLDPC codes is also studied. We show that a CH-GLDPC code in which each variable node is connected to 2 super checks corresponding to a 2-error correcting component code corrects up to 5 errors. The results are also extended to column-weight 4 LDPC codes. Finally, we investigate the eliminating of trapping sets of a column-weight 3 LDPC code using the Gallager B decoding algorithm and generalize the results obtained for the PBF for the Gallager B decoding algorithm.

cs.IT↗

arXiv2015

Majority Logic Decoding under Data-Dependent Logic Gate Failures

A majority logic decoder made of unreliable logic gates, whose failures are transient and datadependent, is analyzed. Based on a combinatorial representation of fault configurations a closed-form expression for the average bit error rate for an one-step majority logic decoder is derived, for a regular low-density parity-check (LDPC) code ensemble and the proposed failure model. The presented analysis framework is then used to establish bounds on the one-step majority logic decoder performance under the simplified probabilistic gate-output switching model. Based on the expander property of Tanner graphs of LDPC codes, it is proven that a version of the faulty parallel bit flipping decoder can correct a fixed fraction of channel errors in the presence of data-dependent gate failures. The results are illustrated with numerical examples of finite geometry codes.

cs.IT↗

arXiv2014

Analysis and Design of Finite Alphabet Iterative Decoders Robust to Faulty Hardware

This paper addresses the problem of designing LDPC decoders robust to transient errors introduced by a faulty hardware. We assume that the faulty hardware introduces errors during the message passing updates and we propose a general framework for the definition of the message update faulty functions. Within this framework, we define symmetry conditions for the faulty functions, and derive two simple error models used in the analysis. With this analysis, we propose a new interpretation of the functional Density Evolution threshold previously introduced, and show its limitations in case of highly unreliable hardware. However, we show that under restricted decoder noise conditions, the functional threshold can be used to predict the convergence behavior of FAIDs under faulty hardware. In particular, we reveal the existence of robust and non-robust FAIDs and propose a framework for the design of robust decoders. We finally illustrate robust and non-robust decoders behaviors of finite length codes using Monte Carlo simulations.

cs.IT↗

arXiv2013

Simplification Resilient LDPC-Coded Sparse-QIM Watermarking for 3D-Meshes

We propose a blind watermarking scheme for 3-D meshes which combines sparse quantization index modulation (QIM) with deletion correction codes. The QIM operates on the vertices in rough concave regions of the surface thus ensuring impeccability, while the deletion correction code recovers the data hidden in the vertices which is removed by mesh optimization and/or simplification. The proposed scheme offers two orders of magnitude better performance in terms of recovered watermark bit error rate compared to the existing schemes of similar payloads and fidelity constraints.

cs.MM↗