Related papers: Decoding Across the Quantum LDPC Code Landscape
Quantum low-density parity-check (QLDPC) codes have been proven to achieve higher minimum distances at higher code rates than surface codes. However, this family of codes imposes stringent latency requirements and poor performance under…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed,…
Hypergraph products are quantum low-density parity-check (LDPC) codes constructed from two classical LDPC codes. Although their dimension and distance depend only on the parameters of the underlying classical codes, optimizing their…
In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain…
We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable…
We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…
In this paper we present a new algorithm, denoted as TEP, to decode low-density parity-check (LDPC) codes over the Binary Erasure Channel (BEC). The TEP decoder is derived applying the expectation propagation (EP) algorithm with a tree-…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
The usual belief propagation (BP) decoders are, in general, exchanging local information on the Tanner graph of the quantum error-correcting (QEC) code and, in particular, are known to not have a threshold for the surface code. We propose…
Hypergraph product codes introduced by Tillich and Z\'emor are a class of quantum LDPC codes with constant rate and distance scaling with the square-root of the block size. Quantum expander codes, a subclass of these codes, can be decoded…
We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore…
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…
We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…