On Quantum-Enhanced LDPC Decoding for Rayleigh Fading Channels

TL;DR

This paper explores quantum-enhanced decoding of LDPC codes over Rayleigh fading channels, formulating the problem as QUBO and using quantum annealing to improve bit error rates compared to classical methods.

Contribution

It introduces a QUBO formulation for LDPC decoding in Rayleigh fading channels and demonstrates performance improvements using quantum annealing with diversity-based postprocessing.

Findings

Quantum annealing improves BER over classical methods.

QUBO formulation enables quantum-classical hybrid decoding.

Diversity in quantum outputs enhances decoding performance.

Abstract

Quantum and Classical computers continue to work together in tight cooperation to solve difficult problems. The combination is thus suggested in recent times for decoding the Low Density Parity Check (LDPC) codes, for the next generation Wireless Communication systems. In this paper we have worked out the Quadratic Unconstrained Binary Optimization (QUBO) formulation for Rayleigh Fading channels for two different scenarios: channel state fully known and not known. The resultant QUBO are solved using D-Wave 2000Q Quantum Annealer and the outputs from the Annealer are classically postprocessed, invoking the notion of diversity. Simple minimum distance decoding of the available copies of the outputs led to improved performance, compared to picking the minimum-energy solution in terms of Bit Error Rate (BER). Apart from providing these results and the comparisons to fully classical Simulated Annealing (SA) and the traditional Belief Propagation (BP) based strategies, some remarks about diversity due to quantum processing are also spelt out.