On Quantum-Assisted LDPC Decoding Augmented with Classical Post-Processing

TL;DR

This paper explores quantum-assisted decoding of LDPC codes using a quantum annealer, combined with classical post-processing, demonstrating improved error rates over traditional methods, especially for larger code lengths.

Contribution

It introduces a novel approach of formulating LDPC decoding as a QUBO problem and employing a quantum annealer with classical post-processing, outperforming classical decoding methods.

Findings

Quantum annealing outperforms belief propagation decoding.

Performance improves with increasing block length.

Reduced error rates at practical SNR levels.

Abstract

Utilizing present and futuristic Quantum Computers to solve difficult problems in different domains has become one of the main endeavors at this moment. Of course, in arriving at the requisite solution both quantum and classical computers work in conjunction. With the continued popularity of Low Density Parity Check (LDPC) codes and hence their decoding, this paper looks into the latter as a Quadratic Unconstrained Binary Optimization (QUBO) and utilized D-Wave 2000Q Quantum Annealer to solve it. The outputs from the Annealer are classically post-processed using simple minimum distance decoding to further improve the performance. We evaluated and compared this implementation against the decoding performance obtained using Simulated Annealing (SA) and belief propagation (BP) decoding with classical computers. The results show that implementations of annealing (both simulated and quantum) are superior to BP decoding and suggest that the advantage becomes more prominent as block lengths increase. Reduced Bit Error Rate (BER) and Frame Error Rate (FER) are observed for simulated annealing and quantum annealing, at useful SNR range - a trend that persists for various codeword lengths.