相关论文: Quantum Quasi-Cyclic LDPC Codes
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
In fault-tolerant quantum computing, quantum algorithms are implemented through quantum circuits capable of error correction. These circuits are typically constructed based on specific quantum error correction codes, with consideration…
We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…
Generalized low-density parity-check (GLDPC) codes, where single parity-check (SPC) constraint nodes are replaced with generalized constraint (GC) nodes, are a promising class of codes for low latency communication. In this paper, a…
More than Mbps secret key rate was demonstrated for continuous-variable quantum key distribution (CV-QKD) systems, but real-time postprocessing is not allowed, which is restricted by the throughput of the error correction decoding in…
We investigate iterative low-resolution message-passing algorithms for quasi-cyclic LDPC codes with horizontal and vertical layered schedules. Coarse quantization and layered scheduling are highly relevant for hardware implementations to…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…
Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…
Error correction is a significant step in postprocessing of continuous-variable quantum key distribution system, which is used to make two distant legitimate parties share identical corrected keys. We propose an experiment demonstration of…
We present a linked-cluster technique for calculating the distance of a quantum LDPC code. It offers an advantage over existing deterministic techniques for codes with small relative distances (which includes all known families of quantum…
To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed. Basic properties of the VS structure are presented.…
We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and shorter length than those designed through classical approaches. The method is extended to time-invariant spatially coupled…
In this study, we report that quantum quasi-cyclic low-density parity-check codes decoded via joint belief propagation (BP) exhibit steep error-rate curves, despite the presence of error floors. To the best of our knowledge, this is the…
Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed…
We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\'emor. For the usual toric codes, we introduce the rotated lattices…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
Minimum distance is an important parameter of a linear error correcting code. For improved performance of binary Low Density Parity Check (LDPC) codes, we need to have the minimum distance grow fast with n, the codelength. However, the best…
Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. To get $q$-ary quantum MDS codes, it suffices to find linear MDS codes $C$ over $\mathbb{F}_{q^2}$ satisfying $C^{\perp_H}\subseteq C$ by the Hermitian…
Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…