Results for “low density parity check code” — Page 2

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2023

Soft syndrome iterative decoding of quantum LDPC codes and hardware architectures

In practical quantum error correction implementations, the measurement of syndrome information is an unreliable step—typically modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this “soft” or analog information to benefit iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation decoders are modified to utilize the soft syndrome to correct both data and syndrome errors simultaneously. We demonstrate the advantages of the proposed scheme not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families but also with faster convergence of iterative decoders. Additionally, we derive hardware (FPGA) architectures of these soft syndrome decoders and obtain similar performance in terms of error correction to the ideal models even with reduced precision in the soft information. The total latency of the hardware architectures is about 600 ns (for the QLDPC codes considered) in a 20 nm CMOS process FPGA device, and the area overhead is almost constant—less than 50% compared to min-sum decoders with noisy syndromes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Soft Syndrome Decoding of Quantum LDPC Codes for Joint Correction of Data and Syndrome Errors

Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are modeled as a binary measurement outcome flipped with some probability. However, the measured syndrome is in fact a discretized value of the continuous voltage or current values obtained in the physical implementation of the syndrome extraction. In this paper, we use this "soft" or analog information without the conventional discretization step to benefit the iterative decoders for decoding quantum low-density parity-check (QLDPC) codes. Syndrome-based iterative belief propagation (BP) decoders are modified to utilize the syndrome-soft information to successfully correct both data and syndrome errors simultaneously, without repeated measurements. We demonstrate the advantages of extracting the soft information from the syndrome in our improved decoders, not only in terms of comparison of thresholds and logical error rates for quasi-cyclic lifted-product QLDPC code families, but also for faster convergence of iterative decoders. In particular, the new BP decoder with noisy syndrome performs as good as the standard BP decoder under ideal syndrome.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

An Assessment of Receiver Algorithms for Distributed Massive MIMO Systems: Investigating Design Solutions and Performance

This study investigates receiver design solutions for distributed Massive Multiple Input Multiple Output (D-m MIMO) systems, taking into account parameters such as number of access points as well as concerns related to channel estimates that use single-carrier frequency-domain equalization (SC-FDE). A significant contribution of this research is the integration of Low-Density Parity-Check (LDPC) codes to simplify coding complexity and enhance communication efficiency. The research examines different receiver designs, such as spatial antenna correlation and sophisticated channel estimation methods. The authors propose integrating LDPC codes into the receiver architecture to simplify computations and enhance error correction and decoding. Moreover, the paper examines performance evaluation measures and approaches, highlighting the trade-offs among complexity, spectral efficiency, and error performance. The comparative analysis indicates the benefits, in terms of performance, of incorporating LDPC codes and improving system throughput and dependability. We examine four distinct receiver algorithms: zero-forcing (ZF), minimum mean square error (MMSE), maximum ratio combining (MRC), and equal gain combining (EGC). The study shows that MRC and EGC receivers work well in D-m MIMO because they make the receiver system less computationally demanding.

Gashtasbi, Ali↗