相关论文: Photonic circuits for iterative decoding of a clas…

The advances in fabrication processes in different material platforms employed in integrated optics are opening the path towards the implementation of circuits with increasing degree of complexity. In addition to the more conventional…

Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…

We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP…

We present a programmable silicon photonic circuit composed of cascaded multiport directional couplers interleaved with thermo-optic phase shifters. The device forms a reconfigurable interferometric network capable of realizing arbitrary $N…

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…

Low Density Parity Check (LDPC) codes are linear error correcting codes used in communication systems for Forward Error Correction (FEC). But, intensive computation is required for encoding and decoding of LDPC codes, making it difficult…

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…

Photonics offers unique advantages as a substrate for quantum information processing, but imposes fundamental scalability challenges. Nondeterministic schemes impose massive resource overheads, while deterministic schemes require…

Algorithms are presented that efficiently shape the parity bits of systematic irregular repeat-accumulate (IRA) low-density parity-check (LDPC) codes by following the sequential encoding order of the accumulator. Simulations over additive…

A design framework to implement non-unitary input-output operations to a practical unitary photonic integrated circuit is described. This is achieved by utilising the cosine-sine decomposition to recover the unitarity of the original…

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing lookup tables replace the conventional operations of the…

The goal of the present paper is the derivation of a framework for the finite-length analysis of message-passing iterative decoding of low-density parity-check codes. To this end we introduce the concept of graph-cover decoding. Whereas in…

We address the problem of performing message-passing-based decoding of quantum LDPC codes under hardware latency limitations. We propose a novel way to do layered decoding that suits quantum constraints and outperforms flooded scheduling,…

Much progress has been made on decoding algorithms for error-correcting codes in the last decade. In this article, we give an introduction to some fundamental results on iterative, message-passing algorithms for low-density parity check…

We propose several improvements for Linear Programming (LP) decoding algorithms for High Density Parity Check (HDPC) codes. First, we use the automorphism groups of a code to create parity check matrix diversity and to generate valid cuts…

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 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…

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the…

We propose and analyze a novel scheme based on LDPC codes for quantitative group testing. The key underlying idea is to augment the bipartite graph by introducing hidden non-binary variables to strengthen the message-passing decoder. This…

We develop a unified theoretical framework for the efficient description of multiphoton states generated and propagating in loop-based optical networks which contain nonlinear elements. These active optical components are modeled as…