Photonic circuits for iterative decoding of a class of low-density parity-check codes

TL;DR

This paper presents a quantum optical photonic circuit model for iterative decoding of expander LDPC codes, demonstrating low-power operation, noise robustness, and performance comparable to classical algorithms, with potential for advanced information processing.

Contribution

It introduces a novel quantum optical circuit architecture for LDPC decoding, leveraging nanophotonic components to enable efficient, noise-tolerant, and low-power iterative decoding algorithms.

Findings

Operates effectively in ultra-low power photonic regimes.

Robust to noise and component imperfections.

Achieves decoding performance comparable to classical algorithms.

Abstract

Photonic circuits in which stateful components are coupled via guided electromagnetic fields are natural candidates for native implementation of iterative stochastic algorithms based on propagation of information around a graph. Conversely, such message passing algorithms suggest novel circuit architectures for signal processing and computation that are well matched to nanophotonic device physics. Here we construct and analyze a quantum optical model of a photonic circuit for iterative decoding of a class of low-density parity-check (LDPC) codes called expander codes. Our circuit can be understood as an open quantum system whose autonomous dynamics map straightforwardly onto the subroutines of an LDPC decoding scheme, with several attractive features: it can operate in the ultra-low power regime of photonics in which quantum fluctuations become significant, is robust to noise and component imperfections, achieves comparable performance to known iterative algorithms for this class of codes, and provides an instructive example of how nanophotonic cavity quantum electrodynamic components can enable useful new information technology even if the solid-state qubits on which they are based are heavily dephased and cannot support large-scale entanglement.