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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…
The performance of maximum-likelihood (ML) decoding on the binary erasure channel for finite-length low-density parity-check (LDPC) codes from two random ensembles is studied. The theoretical average spectrum of the Gallager ensemble is…
In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…
We propose a new type of ultimate-Shannon-limit-approaching codes called spatially coupled protograph-based low-density parity-check Hadamard convolutional codes (SC-PLDPCH-CCs), which are constructed by spatially coupling PLDPC-Hadamard…
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.…
A variation of low density parity check (LDPC) error correcting codes defined over Galois fields ($GF(q)$) is investigated using statistical physics. A code of this type is characterised by a sparse random parity check matrix composed of…
Distributed storage systems suffer from significant repair traffic generated due to frequent storage node failures. This paper shows that properly designed low-density parity-check (LDPC) codes can substantially reduce the amount of…
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most…
We consider generalized low-density parity-check (GLDPC) codes with component codes that are duals of Cordaro-Wagner codes. Two efficient decoding algorithms are proposed: one based on Hartmann-Rudolph processing, analogous to Sum-Product…
Consider an ensemble of regular generalized LDPC (GLDPC) codes and assume that the same component code is associated with each parity check node. To decode a GLDPC code from the ensemble, we use the bit flipping bounded distance decoding…
Families of generalized spatially-coupled low-density parity-check (GSC-LDPC) code ensembles can be formed by terminating protograph-based generalized LDPC convolutional (GLDPCC) codes. It has previously been shown that ensembles of…
This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density…
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. The aim of LP decoding is to develop an algorithm which has error-correcting performance…
Although high-threshold and low-overhead quantum low-density parity-check (qLDPC) codes, such as bivariate bicycle (BB) codes, can reduce the physical-qubit cost by an order of magnitude compared to the Kitaev toric code, their torus layout…
We propose a deterministic method to design irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels (BEC). Compared to the existing methods, which are based on the application of asymptomatic analysis tools such as…
Low-density parity-check (LDPC) codes form part of the IRIG-106 standard and have been successfully deployed for the Telemetry Group version of shaped-offset quadrature phase shift keying (SOQPSK-TG) modulation. Recently, LDPC code…
In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…
Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
Polarization-adjusted convolutional (PAC) codes can approach the theoretical bound for block error rate (BLER) performance at short-to-medium codeword length. PAC codes have excellent BLER performance using Monte Carlo (MC) rate-profiles…