Related papers: An Efficient Algorithm to Sample Quantum Low-Densi…

The asymptotic iterative decoding performances of low-density parity-check (LDPC) codes using min-sum (MS) and sum-product (SP) decoding algorithms on memoryless binary-input output-symmetric (MBIOS) channels are analyzed in this paper. For…

In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…

In this paper, we present a novel way for solving the main problem of designing the capacity approaching irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). The proposed method is much simpler, faster,…

Decoders for Low Density Parity Check (LDPC) codes are usually tailored to an application and optimized once the specific content and structure of the parity matrix are known. In this work we consider the parity matrix as an argument of the…

This paper is concerned with the construction of low-density parity-check (LDPC) codes with low error floors. Two main contributions are made. First, a new class of structured LDPC codes is introduced. The parity check matrices of these…

A quantized message passing decoding algorithm for low-density parity-check codes is presented. The algorithm relies on the min approximation at the check nodes, and on modelling the variable node inbound messages as observations of an…

Simulating fermionic systems on qubit-based quantum computers often demands significant computational resources due to the requirement to map fermions to qubits. Thus, designing a fault-tolerant quantum computer that operates directly with…

This paper is concerned with linear superposition systems in which all components of the superimposed signal are coded with an identical binary low-density parity-check (LDPC) code.

A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…

Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…

The decoding throughput in the postprocessing is one of the bottlenecks for a continuous-variable quantum key distribution (CV-QKD) system. In this paper, we propose a layered decoder to decode quasi-cyclic multi-edge type LDPC (QC-METLDPC)…

In a previous work, we presented a parallel encoding algorithm for low-density parity-check (LDPC) codes by partitioning hypergraph representation for the LDPC codes. The aim of this research is to analyze the processing time of this…

Many entanglement distillation schemes use either universal random hashing or breeding as their final step to obtain almost perfect shared EPR pairs. In spite of a high yield, the hardness of decoding a random linear code makes the use of…

We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a `small-world' lattice. We apply our…

In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief…

We consider an information reconciliation protocol for quantum key distribution (QKD). In order to correct down the error rate, we suggest a method, which is based on symmetric blind information reconciliation for the low-density…

LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as…

We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal…

We present an analysis, under iterative decoding, of coset LDPC codes over GF(q), designed for use over arbitrary discrete-memoryless channels (particularly nonbinary and asymmetric channels). We use a random-coset analysis to produce an…

In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…