Towards Quantum Belief Propagation for LDPC Decoding in Wireless Networks

TL;DR

This paper introduces Quantum Belief Propagation (QBP), a quantum annealing-based LDPC decoder that improves error rates and decoding speed over classical methods, demonstrating potential for future wireless communication systems.

Contribution

The paper presents a novel quantum annealing-based LDPC decoding method, QBP, capable of supporting block lengths up to 420 bits and achieving significant error rate improvements over FPGA-based decoders.

Findings

QBP achieves a bit error rate of 10^{-8} in 20 μs.

QBP reaches a frame error rate of 10^{-6} in 50 μs at SNR 9 dB.

QBP outperforms FPGA-based decoders at lower SNRs.

Abstract

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of $10^{-8}$ in 20 $\mu$s and a 1,500 byte frame error rate of $10^{-6}$ in 50 $\mu$s at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 $\mu$s to achieve a 1,500 byte 99.99$\%$ frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of $10^{-8}$ and a frame error rate of $10^{-6}$ at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized ($\textit{e.g.,}$ Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations.