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Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are…
Layered decoding is well appreciated in Low-Density Parity-Check (LDPC) decoder implementation since it can achieve effectively high decoding throughput with low computation complexity. This work, for the first time, addresses low…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding…
In the search for highly efficient decoders for short LDPC codes approaching maximum likelihood performance, a relayed decoding strategy, specifically activating the ordered statistics decoding process upon failure of a neural min-sum…
Learning-based image compression has improved to a level where it can outperform traditional image codecs such as HEVC and VVC in terms of coding performance. In addition to good compression performance, device interoperability is essential…
Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity…
We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…
We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous…
Reconciliation is a crucial procedure in post-processing of Quantum Key Distribution (QKD), which is used for correcting the error bits in sifted key strings. Although most studies about reconciliation of QKD focus on how to improve the…
Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…
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…
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this…
Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations…
Quantum low-density parity-check (qLDPC) codes are promising for realizing scalable fault-tolerant quantum computation due to their potential for low-overhead protocols. A common approach to decoding qLDPC codes is to use the belief…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
The development of multicore architectures supporting parallel data processing has led to a paradigm shift, which affects communication systems significantly. This article provides a scalable parallel approach of an iterative LDPC decoder,…
Imperfect measurements are a prevalent source of error across quantum computing platforms, significantly degrading the logical error rates achievable on current hardware. To mitigate this issue, rich measurement data referred to as soft…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
In this study, an optimization model for offline scheduling policy of low-density parity-check (LDPC) codes is proposed to improve the decoding efficiency of the belief propagation (BP). The optimization model uses the number of messages…