Related papers: Spatially Coupled Quasi-Cyclic Quantum LDPC Codes
In this paper, we present a new method for explicitly constructing regular low-density parity-check (LDPC) codes based on $\mathbb{S}_{n}(\mathbb{F}_{q})$, the space of $n\times n$ symmetric matrices over $\mathbb{F}_{q}$. Using this…
Low-density parity check (LDPC) codes are an important class of codes with many applications. Two algebraic methods for constructing regular LDPC codes are derived -- one based on nonprimitive narrow-sense BCH codes and the other directly…
Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at…
We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes over integer residue rings and analyze their performance with respect to the Lee metric. Their…
Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth.…
Low-density parity-check (LDPC) codes are capable of achieving excellent performance and provide a useful alternative for high performance applications. However, at medium to high signal-to-noise ratios (SNR), an observable error floor…
Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental…
We investigate the minimum distance of structured binary Low-Density Parity-Check (LDPC) codes whose parity-check matrices are of the form $[\mathbf{C} \vert \mathbf{M}]$ where $\mathbf{C}$ is circulant and of column weight $2$, and…
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…
With the development of quantum error correction techniques, quantum low density parity check (QLDPC) codes become a promising area in quantum error correction codes. In this paper, the requirements of QLDPC codes based on points except the…
The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block…
Recent works showed how low-density parity-check (LDPC) erasure correcting codes, under maximum likelihood (ML) decoding, are capable of tightly approaching the performance of an ideal maximum-distance-separable code on the binary erasure…
In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates.…
We propose a method for modifying orthogonal sparse matrix pairs used in CSS codes while preserving their matrix row and column weight distributions, which play a crucial role in determining the performance of belief-propagation decoding.…
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in…
We present the Low Density Parity Check (LDPC) forward error correction algorithm adapted for the Quantum Key Distribution (QKD) protocol in a form readily applied by developers. A sparse parity check matrix is required for the LDPC…
Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that have excellent performance thanks to the degrees of freedom they offer. An SC code is designed by partitioning a base matrix into components, the number…